LMFDB - Embedded newform 4.35.b.a.3.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,35,Mod(3,4)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 35, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 35);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 35 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$29.2902616171$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 72626617369828 x^{14} - 508386321588656 x^{13} + \cdots + 10\!\cdots\!04 $ x^16 - 8x^15 + 72626617369828x^14 - 508386321588656x^13 + 2070719277905647749353609238x^12 - 12424315667427277473941003264x^11 + 29149279164108071001422670079476973946124x^10 - 145746395820426465446828612470414408396048x^9 + 208496096173568297991996731996084596831140332539876641x^8 - 833984384693398713593064505859129757329019844492402808x^7 + 698875044281632666404075222255491833772167721683562957908849313992x^6 - 2096625132841979053865799383403762221200483615238531437571184911168x^5 + 875349684493967266675808505113830711763013718564229702361030689486070549970192x^4 - 1750699368984440158130214684786333899894027567027597503857227657836248590530944x^3 + 58492108779558800474886843372761385704540074687283929338876917776255190499572053123416832x^2 - 58492108778683450790394972731218418552991821255044754502302019047778482600406279068669952*x + 1002905835814255424301301646724378424153530387112307506080792395282136017819372496998790246522159104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{240}\cdot 3^{26}\cdot 5^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.14
Root			$0.500000 - 1.72842e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.35.b.a.3.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(114483. + 63824.3i) q^{2} +8.29643e7i q^{3} +(9.03280e9 + 1.46136e10i) q^{4} +6.47366e11 q^{5} +(-5.29513e12 + 9.49799e12i) q^{6} +1.29684e14i q^{7} +(1.01400e14 + 2.24952e15i) q^{8} +9.79411e15 q^{9} +O(q^{10})$	\(q+(114483. + 63824.3i) q^{2} +8.29643e7i q^{3} +(9.03280e9 + 1.46136e10i) q^{4} +6.47366e11 q^{5} +(-5.29513e12 + 9.49799e12i) q^{6} +1.29684e14i q^{7} +(1.01400e14 + 2.24952e15i) q^{8} +9.79411e15 q^{9} +(7.41124e16 + 4.13177e16i) q^{10} -3.33547e16i q^{11} +(-1.21240e18 + 7.49399e17i) q^{12} +8.70180e18 q^{13} +(-8.27701e18 + 1.48467e19i) q^{14} +5.37083e19i q^{15} +(-1.31965e20 + 2.64003e20i) q^{16} -4.22830e20 q^{17} +(1.12126e21 + 6.25102e20i) q^{18} +4.20554e21i q^{19} +(5.84753e21 + 9.46034e21i) q^{20} -1.07592e22 q^{21} +(2.12884e21 - 3.81855e21i) q^{22} -2.57146e23i q^{23} +(-1.86629e23 + 8.41259e21i) q^{24} -1.62993e23 q^{25} +(9.96207e23 + 5.55386e23i) q^{26} +2.19617e24i q^{27} +(-1.89515e24 + 1.17141e24i) q^{28} -4.39836e24 q^{29} +(-3.42789e24 + 6.14868e24i) q^{30} +3.47904e25i q^{31} +(-3.19575e25 + 2.18012e25i) q^{32} +2.76725e24 q^{33} +(-4.84068e25 - 2.69868e25i) q^{34} +8.39534e25i q^{35} +(8.84682e25 + 1.43127e26i) q^{36} -5.87647e26 q^{37} +(-2.68415e26 + 4.81462e26i) q^{38} +7.21938e26i q^{39} +(6.56431e25 + 1.45626e27i) q^{40} +1.01906e27 q^{41} +(-1.23174e27 - 6.86696e26i) q^{42} -2.83471e27i q^{43} +(4.87432e26 - 3.01287e26i) q^{44} +6.34038e27 q^{45} +(1.64121e28 - 2.94388e28i) q^{46} -2.29098e28i q^{47} +(-2.19028e28 - 1.09484e28i) q^{48} +3.72989e28 q^{49} +(-1.86599e28 - 1.04029e28i) q^{50} -3.50798e28i q^{51} +(7.86016e28 + 1.27164e29i) q^{52} +1.06357e29 q^{53} +(-1.40169e29 + 2.51424e29i) q^{54} -2.15927e28i q^{55} +(-2.91727e29 + 1.31500e28i) q^{56} -3.48909e29 q^{57} +(-5.03537e29 - 2.80722e29i) q^{58} -4.19589e28i q^{59} +(-7.84870e29 + 4.85136e29i) q^{60} +3.59417e30 q^{61} +(-2.22047e30 + 3.98291e30i) q^{62} +1.27014e30i q^{63} +(-5.05004e30 + 4.56202e29i) q^{64} +5.63325e30 q^{65} +(3.16803e29 + 1.76618e29i) q^{66} -1.73917e31i q^{67} +(-3.81934e30 - 6.17906e30i) q^{68} +2.13339e31 q^{69} +(-5.35826e30 + 9.61122e30i) q^{70} -4.95397e31i q^{71} +(9.93125e29 + 2.20320e31i) q^{72} +8.07839e31 q^{73} +(-6.72755e31 - 3.75061e31i) q^{74} -1.35226e31i q^{75} +(-6.14579e31 + 3.79878e31i) q^{76} +4.32559e30 q^{77} +(-4.60772e31 + 8.26496e31i) q^{78} +2.83994e32i q^{79} +(-8.54298e31 + 1.70907e32i) q^{80} -1.88656e31 q^{81} +(1.16665e32 + 6.50411e31i) q^{82} -2.69083e32i q^{83} +(-9.71854e31 - 1.57230e32i) q^{84} -2.73726e32 q^{85} +(1.80923e32 - 3.24525e32i) q^{86} -3.64907e32i q^{87} +(7.50320e31 - 3.38218e30i) q^{88} -3.78316e32 q^{89} +(7.25865e32 + 4.04670e32i) q^{90} +1.12849e33i q^{91} +(3.75782e33 - 2.32275e33i) q^{92} -2.88636e33 q^{93} +(1.46220e33 - 2.62278e33i) q^{94} +2.72252e33i q^{95} +(-1.80872e33 - 2.65133e33i) q^{96} +1.06366e33 q^{97} +(4.27009e33 + 2.38057e33i) q^{98} -3.26680e32i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots - 67\!\cdots\!80 q^{9}+O(q^{10}) $ 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9	$ 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots + 16\!\cdots\!32 q^{98}+O(q^{100}) $ 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9 - 45113792455239160 * q^10 + 2389205919902175360 * q^12 - 5233507036411659616 * q^13 - 78584294183795706432 * q^14 + 495182112183820124416 * q^16 - 603670905919309938144 * q^17 - 3049682100893194226508 * q^18 - 33058393758449688290400 * q^20 + 51436061805005728413696 * q^21 + 71660876143050404765280 * q^22 + 216144869785928938234368 * q^24 + 1224730607199300816400560 * q^25 - 2068583291215840445568696 * q^26 + 891252510406495618671360 * q^28 - 4086289565288128397679456 * q^29 + 29601064663371600024444480 * q^30 + 20026414012547463259849728 * q^32 + 73954448514753271238568960 * q^33 + 46288216238217191722231976 * q^34 + 569062048300724903070378384 * q^36 + 950385175701396416644593056 * q^37 - 123498782719680108073563360 * q^38 - 3250024485723791435879459200 * q^40 + 469238845433510127731349792 * q^41 + 2352670327884382399711157760 * q^42 + 7327222247557584897899214720 * q^44 - 24427097188106605438098250080 * q^45 - 19562783684402230406331003072 * q^46 + 10576141603633237485164267520 * q^48 - 5662649722408510114314091760 * q^49 + 20191932196464263485504736220 * q^50 - 299155663662273783907276503904 * q^52 - 287274278887575172234950512736 * q^53 + 6047252470624543429578889536 * q^54 + 957626384837555513184792726528 * q^56 + 2791286265941381406754467578880 * q^57 - 314499391713380785247660833336 * q^58 + 1103184540481814815474103512320 * q^60 - 7360215904797065436447249778528 * q^61 + 6668101684324825273374014288640 * q^62 - 4672502276277215477475812569088 * q^64 + 7390500022468645317433010287680 * q^65 - 12460359580334220374288279205120 * q^66 + 3201090312765007118305938045984 * q^68 - 20909099675706939600670541666304 * q^69 - 13302319794857519494110175324800 * q^70 - 776423968147266229824274003392 * q^72 - 21322365514881309087265291408096 * q^73 + 60200090281780873185690769101576 * q^74 - 104909582027053727863743869884800 * q^76 + 31510097566037837419459121448960 * q^77 + 173718506967281862717403400063040 * q^78 + 360511559214548868760655536888320 * q^80 - 262819454584631237298859074129648 * q^81 - 127799686177535642546403976474264 * q^82 - 481860976739335096182940424300544 * q^84 + 2066519418228326883252673443837760 * q^85 + 680164732953303409567751182232928 * q^86 - 1868588957981221169228370505105920 * q^88 - 2487774705888249186282098457137376 * q^89 + 2710136859758550244207319911170120 * q^90 - 5719642193953545223478177490435840 * q^92 - 4648987096869411453766406983557120 * q^93 - 174301665834847119752293250078592 * q^94 - 1356265248520894619800195113541632 * q^96 + 7119191713926779638291321673063456 * q^97 + 16929214407930779244441537548523732 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	114483.	+	63824.3i	0.873435	+	0.486940i
$2$	114483.	+	63824.3i	0.873435	+	0.486940i
$3$			8.29643e7i			0.642436i	0.947005	+	0.321218i	$0.104092\pi$
$3$			8.29643e7i			0.642436i	−0.947005	+	0.321218i	$0.895908\pi$
$4$	9.03280e9	+	1.46136e10i	0.525778	+	0.850622i
$5$	6.47366e11			0.848516			0.424258	−	0.905541i	$-0.360535\pi$
$5$	6.47366e11			0.848516			0.424258	+	0.905541i	$0.360535\pi$
$6$	−5.29513e12	+	9.49799e12i	−0.312828	+	0.561126i
$7$			1.29684e14i			0.557470i	0.960368	+	0.278735i	$0.0899151\pi$
$7$			1.29684e14i			0.557470i	−0.960368	+	0.278735i	$0.910085\pi$
$8$	1.01400e14	+	2.24952e15i	0.0450307	+	0.998986i
$9$	9.79411e15			0.587276
$10$	7.41124e16	+	4.13177e16i	0.741124	+	0.413177i
$11$		−	3.33547e16i		−	0.0659906i	−0.999456	−	0.0329953i	$-0.989495\pi$
$11$		−	3.33547e16i		−	0.0659906i	0.999456	−	0.0329953i	$-0.0105046\pi$
$12$	−1.21240e18	+	7.49399e17i	−0.546470	+	0.337779i
$13$	8.70180e18			1.00594			0.502970	−	0.864304i	$-0.332241\pi$
$13$	8.70180e18			1.00594			0.502970	+	0.864304i	$0.332241\pi$
$14$	−8.27701e18	+	1.48467e19i	−0.271455	+	0.486914i
$15$			5.37083e19i			0.545117i
$16$	−1.31965e20	+	2.64003e20i	−0.447115	+	0.894476i
$17$	−4.22830e20			−0.511134			−0.255567	−	0.966791i	$-0.582262\pi$
$17$	−4.22830e20			−0.511134			−0.255567	+	0.966791i	$0.582262\pi$
$18$	1.12126e21	+	6.25102e20i	0.512948	+	0.285969i
$19$			4.20554e21i			0.767379i	0.923462	+	0.383690i	$0.125347\pi$
$19$			4.20554e21i			0.767379i	−0.923462	+	0.383690i	$0.874653\pi$
$20$	5.84753e21	+	9.46034e21i	0.446131	+	0.721766i
$21$	−1.07592e22			−0.358138
$22$	2.12884e21	−	3.81855e21i	0.0321335	−	0.0576385i
$23$		−	2.57146e23i		−	1.82308i	−0.411209	−	0.911541i	$-0.634893\pi$
$23$		−	2.57146e23i		−	1.82308i	0.411209	−	0.911541i	$-0.365107\pi$
$24$	−1.86629e23	+	8.41259e21i	−0.641784	+	0.0289293i
$25$	−1.62993e23			−0.280020
$26$	9.96207e23	+	5.55386e23i	0.878623	+	0.489833i
$27$			2.19617e24i			1.01972i
$28$	−1.89515e24	+	1.17141e24i	−0.474196	+	0.293105i
$29$	−4.39836e24			−0.606072			−0.303036	−	0.952979i	$-0.598000\pi$
$29$	−4.39836e24			−0.606072			−0.303036	+	0.952979i	$0.598000\pi$
$30$	−3.42789e24	+	6.14868e24i	−0.265440	+	0.476124i
$31$			3.47904e25i			1.54281i	0.636347	+	0.771403i	$0.280445\pi$
$31$			3.47904e25i			1.54281i	−0.636347	+	0.771403i	$0.719555\pi$
$32$	−3.19575e25	+	2.18012e25i	−0.826083	+	0.563549i
$33$	2.76725e24			0.0423947
$34$	−4.84068e25	−	2.69868e25i	−0.446442	−	0.248892i
$35$			8.39534e25i			0.473022i
$36$	8.84682e25	+	1.43127e26i	0.308777	+	0.499550i
$37$	−5.87647e26			−1.28732			−0.643661	−	0.765311i	$-0.722585\pi$
$37$	−5.87647e26			−1.28732			−0.643661	+	0.765311i	$0.722585\pi$
$38$	−2.68415e26	+	4.81462e26i	−0.373668	+	0.670256i
$39$			7.21938e26i			0.646252i
$40$	6.56431e25	+	1.45626e27i	0.0382093	+	0.847655i
$41$	1.01906e27			0.389831			0.194915	−	0.980820i	$-0.437557\pi$
$41$	1.01906e27			0.389831			0.194915	+	0.980820i	$0.437557\pi$
$42$	−1.23174e27	−	6.86696e26i	−0.312811	−	0.174392i
$43$		−	2.83471e27i		−	0.482552i	−0.970457	−	0.241276i	$-0.922434\pi$
$43$		−	2.83471e27i		−	0.482552i	0.970457	−	0.241276i	$-0.0775659\pi$
$44$	4.87432e26	−	3.01287e26i	0.0561330	−	0.0346964i
$45$	6.34038e27			0.498313
$46$	1.64121e28	−	2.94388e28i	0.887733	−	1.59234i
$47$		−	2.29098e28i		−	0.859722i	−0.902895	−	0.429861i	$-0.858563\pi$
$47$		−	2.29098e28i		−	0.859722i	0.902895	−	0.429861i	$-0.141437\pi$
$48$	−2.19028e28	−	1.09484e28i	−0.574644	−	0.287243i
$49$	3.72989e28			0.689228
$50$	−1.86599e28	−	1.04029e28i	−0.244580	−	0.136353i
$51$		−	3.50798e28i		−	0.328370i
$52$	7.86016e28	+	1.27164e29i	0.528901	+	0.855674i
$53$	1.06357e29			0.517698			0.258849	−	0.965918i	$-0.416657\pi$
$53$	1.06357e29			0.517698			0.258849	+	0.965918i	$0.416657\pi$
$54$	−1.40169e29	+	2.51424e29i	−0.496544	+	0.890662i
$55$		−	2.15927e28i		−	0.0559941i
$56$	−2.91727e29	+	1.31500e28i	−0.556904	+	0.0251033i
$57$	−3.48909e29			−0.492992
$58$	−5.03537e29	−	2.80722e29i	−0.529365	−	0.295121i
$59$		−	4.19589e28i		−	0.0329868i	−0.999864	−	0.0164934i	$-0.994750\pi$
$59$		−	4.19589e28i		−	0.0329868i	0.999864	−	0.0164934i	$-0.00525025\pi$
$60$	−7.84870e29	+	4.85136e29i	−0.463689	+	0.286611i
$61$	3.59417e30			1.60322			0.801608	−	0.597851i	$-0.203978\pi$
$61$	3.59417e30			1.60322			0.801608	+	0.597851i	$0.203978\pi$
$62$	−2.22047e30	+	3.98291e30i	−0.751254	+	1.34754i
$63$			1.27014e30i			0.327389i
$64$	−5.05004e30	+	4.56202e29i	−0.995944	+	0.0899701i
$65$	5.63325e30			0.853556
$66$	3.16803e29	+	1.76618e29i	0.0370290	+	0.0206437i
$67$		−	1.73917e31i		−	1.57424i	−0.616803	−	0.787118i	$-0.711572\pi$
$67$		−	1.73917e31i		−	1.57424i	0.616803	−	0.787118i	$-0.288428\pi$
$68$	−3.81934e30	−	6.17906e30i	−0.268743	−	0.434781i
$69$	2.13339e31			1.17121
$70$	−5.35826e30	+	9.61122e30i	−0.230334	+	0.413154i
$71$		−	4.95397e31i		−	1.67325i	−0.547773	−	0.836627i	$-0.684524\pi$
$71$		−	4.95397e31i		−	1.67325i	0.547773	−	0.836627i	$-0.315476\pi$
$72$	9.93125e29	+	2.20320e31i	0.0264455	+	0.586680i
$73$	8.07839e31			1.70152			0.850759	−	0.525557i	$-0.176143\pi$
$73$	8.07839e31			1.70152			0.850759	+	0.525557i	$0.176143\pi$
$74$	−6.72755e31	−	3.75061e31i	−1.12439	−	0.626849i
$75$		−	1.35226e31i		−	0.179895i
$76$	−6.14579e31	+	3.79878e31i	−0.652750	+	0.403471i
$77$	4.32559e30			0.0367878
$78$	−4.60772e31	+	8.26496e31i	−0.314686	+	0.564459i
$79$			2.83994e32i			1.56189i	0.624602	+	0.780943i	$0.285261\pi$
$79$			2.83994e32i			1.56189i	−0.624602	+	0.780943i	$0.714739\pi$
$80$	−8.54298e31	+	1.70907e32i	−0.379384	+	0.758978i
$81$	−1.88656e31			−0.0678304
$82$	1.16665e32	+	6.50411e31i	0.340492	+	0.189824i
$83$		−	2.69083e32i		−	0.639085i	−0.947572	−	0.319543i	$-0.896471\pi$
$83$		−	2.69083e32i		−	0.639085i	0.947572	−	0.319543i	$-0.103529\pi$
$84$	−9.71854e31	−	1.57230e32i	−0.188301	−	0.304640i
$85$	−2.73726e32			−0.433705
$86$	1.80923e32	−	3.24525e32i	0.234974	−	0.421478i
$87$		−	3.64907e32i		−	0.389363i
$88$	7.50320e31	−	3.38218e30i	0.0659237	−	0.00297160i
$89$	−3.78316e32			−0.274299			−0.137150	−	0.990550i	$-0.543794\pi$
$89$	−3.78316e32			−0.274299			−0.137150	+	0.990550i	$0.543794\pi$
$90$	7.25865e32	+	4.04670e32i	0.435244	+	0.242649i
$91$			1.12849e33i			0.560781i
$92$	3.75782e33	−	2.32275e33i	1.55075	−	0.958536i
$93$	−2.88636e33			−0.991153
$94$	1.46220e33	−	2.62278e33i	0.418633	−	0.750911i
$95$			2.72252e33i			0.651134i
$96$	−1.80872e33	−	2.65133e33i	−0.362044	−	0.530705i
$97$	1.06366e33			0.178519			0.0892594	−	0.996008i	$-0.471550\pi$
$97$	1.06366e33			0.178519			0.0892594	+	0.996008i	$0.471550\pi$
$98$	4.27009e33	+	2.38057e33i	0.601996	+	0.335613i
$99$		−	3.26680e32i		−	0.0387547i
$100$	−1.47229e33	−	2.38191e33i	−0.147229	−	0.238191i
$101$	−1.65994e34			−1.40162			−0.700808	−	0.713350i	$-0.747177\pi$
$101$	−1.65994e34			−1.40162			−0.700808	+	0.713350i	$0.747177\pi$
$102$	2.23894e33	−	4.01604e33i	0.159897	−	0.286810i
$103$			9.46712e32i			0.0572776i	0.999590	+	0.0286388i	$0.00911726\pi$
$103$			9.46712e32i			0.0572776i	−0.999590	+	0.0286388i	$0.990883\pi$
$104$	8.82364e32	+	1.95748e34i	0.0452982	+	1.00492i
$105$	−6.96513e33			−0.303886
$106$	1.21761e34	+	6.78816e33i	0.452176	+	0.252088i
$107$			4.09666e34i			1.29690i	0.761259	+	0.648448i	$0.224582\pi$
$107$			4.09666e34i			1.29690i	−0.761259	+	0.648448i	$0.775418\pi$
$108$	−3.20939e34	+	1.98376e34i	−0.867399	+	0.536148i
$109$	1.87027e34			0.432169			0.216084	−	0.976375i	$-0.430671\pi$
$109$	1.87027e34			0.432169			0.216084	+	0.976375i	$0.430671\pi$
$110$	1.37814e33	−	2.47200e33i	0.0272658	−	0.0489072i
$111$		−	4.87537e34i		−	0.827021i
$112$	−3.42371e34	−	1.71138e34i	−0.498643	−	0.249253i
$113$	1.19952e35			1.50202			0.751010	−	0.660291i	$-0.229567\pi$
$113$	1.19952e35			1.50202			0.751010	+	0.660291i	$0.229567\pi$
$114$	−3.99441e34	−	2.22689e34i	−0.430597	−	0.240058i
$115$		−	1.66468e35i		−	1.54691i
$116$	−3.97295e34	−	6.42757e34i	−0.318660	−	0.515539i
$117$	8.52264e34			0.590765
$118$	2.67800e33	−	4.80358e33i	0.0160626	−	0.0288118i
$119$		−	5.48345e34i		−	0.284941i
$120$	−1.20818e35	+	5.44603e33i	−0.544564	+	0.0245470i
$121$	2.54364e35			0.995645
$122$	4.11471e35	+	2.29395e35i	1.40030	+	0.780670i
$123$			8.45460e34i			0.250441i
$124$	−5.08413e35	+	3.14255e35i	−1.31234	+	0.811173i
$125$	−4.82333e35			−1.08612
$126$	−8.10660e34	+	1.45410e35i	−0.159419	+	0.285953i
$127$		−	3.85585e34i		−	0.0662914i	−0.999451	−	0.0331457i	$-0.989447\pi$
$127$		−	3.85585e34i		−	0.0662914i	0.999451	−	0.0331457i	$-0.0105525\pi$
$128$	−6.07260e35	−	2.70088e35i	−0.913703	−	0.406383i
$129$	2.35179e35			0.310009
$130$	6.44911e35	+	3.59538e35i	0.745526	+	0.415631i
$131$			8.06433e35i			0.818382i	0.912449	+	0.409191i	$0.134189\pi$
$131$			8.06433e35i			0.818382i	−0.912449	+	0.409191i	$0.865811\pi$
$132$	2.49960e34	+	4.04394e34i	0.0222902	+	0.0360619i
$133$	−5.45393e35			−0.427791
$134$	1.11001e36	−	1.99105e36i	0.766559	−	1.37499i
$135$			1.42173e36i			0.865251i
$136$	−4.28751e34	−	9.51163e35i	−0.0230167	−	0.510615i
$137$	−3.19441e36			−1.51405			−0.757026	−	0.653385i	$-0.773348\pi$
$137$	−3.19441e36			−1.51405			−0.757026	+	0.653385i	$0.773348\pi$
$138$	2.44237e36	+	1.36162e36i	1.02298	+	0.570311i
$139$		−	1.92587e36i		−	0.713469i	−0.934206	−	0.356735i	$-0.883890\pi$
$139$		−	1.92587e36i		−	0.713469i	0.934206	−	0.356735i	$-0.116110\pi$
$140$	−1.22686e36	+	7.58334e35i	−0.402363	+	0.248705i
$141$	1.90070e36			0.552316
$142$	3.16184e36	−	5.67145e36i	0.814775	−	1.46148i
$143$		−	2.90246e35i		−	0.0663826i
$144$	−1.29248e36	+	2.58567e36i	−0.262580	+	0.525305i
$145$	−2.84735e36			−0.514262
$146$	9.24838e36	+	5.15597e36i	1.48616	+	0.828538i
$147$			3.09448e36i			0.442784i
$148$	−5.30809e36	−	8.58762e36i	−0.676845	−	1.09502i
$149$	1.47472e36			0.167704			0.0838521	−	0.996478i	$-0.473278\pi$
$149$	1.47472e36			0.167704			0.0838521	+	0.996478i	$0.473278\pi$
$150$	8.63071e35	−	1.54811e36i	0.0875982	−	0.157127i
$151$		−	1.17710e37i		−	1.06710i	−0.845769	−	0.533549i	$-0.820858\pi$
$151$		−	1.17710e37i		−	1.06710i	0.845769	−	0.533549i	$-0.179142\pi$
$152$	−9.46042e36	+	4.26442e35i	−0.766601	+	0.0345556i
$153$	−4.14125e36			−0.300177
$154$	4.95206e35	+	2.76078e35i	0.0321317	+	0.0179134i
$155$			2.25222e37i			1.30910i
$156$	−1.05501e37	+	6.52112e36i	−0.549716	+	0.339785i
$157$	1.63675e37			0.765046			0.382523	−	0.923946i	$-0.375055\pi$
$157$	1.63675e37			0.765046			0.382523	+	0.923946i	$0.375055\pi$
$158$	−1.81257e37	+	3.25125e37i	−0.760545	+	1.36421i
$159$			8.82384e36i			0.332588i
$160$	−2.06882e37	+	1.41134e37i	−0.700945	+	0.478180i
$161$	3.33478e37			1.01631
$162$	−2.15978e36	−	1.20408e36i	−0.0592455	−	0.0330294i
$163$		−	3.99721e37i		−	0.987569i	−0.869584	−	0.493785i	$-0.835613\pi$
$163$		−	3.99721e37i		−	0.987569i	0.869584	−	0.493785i	$-0.164387\pi$
$164$	9.20500e36	+	1.48922e37i	0.204964	+	0.331599i
$165$	1.79143e36			0.0359726
$166$	1.71740e37	−	3.08054e37i	0.311196	−	0.558199i
$167$		−	9.71671e37i		−	1.58979i	−0.606748	−	0.794894i	$-0.707526\pi$
$167$		−	9.71671e37i		−	1.58979i	0.606748	−	0.794894i	$-0.292474\pi$
$168$	−1.09098e36	−	2.42029e37i	−0.0161272	−	0.357775i
$169$	8.91592e35			0.0119150
$170$	−3.13370e37	−	1.74704e37i	−0.378813	−	0.211189i
$171$			4.11895e37i			0.450664i
$172$	4.14252e37	−	2.56053e37i	0.410469	−	0.253715i
$173$	6.61410e37			0.593864			0.296932	−	0.954899i	$-0.404037\pi$
$173$	6.61410e37			0.593864			0.296932	+	0.954899i	$0.404037\pi$
$174$	2.32899e37	−	4.17756e37i	0.189596	−	0.340083i
$175$		−	2.11377e37i		−	0.156103i
$176$	8.80575e36	+	4.40166e36i	0.0590270	+	0.0295054i
$177$	3.48109e36			0.0211919
$178$	−4.33107e37	−	2.41458e37i	−0.239583	−	0.133568i
$179$			2.38286e38i			1.19839i	0.800604	+	0.599194i	$0.204512\pi$
$179$			2.38286e38i			1.19839i	−0.800604	+	0.599194i	$0.795488\pi$
$180$	5.72714e37	+	9.26556e37i	0.262002	+	0.423876i
$181$	−3.55657e38			−1.48080			−0.740399	−	0.672168i	$-0.765363\pi$
$181$	−3.55657e38			−1.48080			−0.740399	+	0.672168i	$0.765363\pi$
$182$	−7.20249e37	+	1.29193e38i	−0.273067	+	0.489806i
$183$			2.98188e38i			1.02996i
$184$	5.78454e38	−	2.60746e37i	1.82123	−	0.0820947i
$185$	−3.80423e38			−1.09231
$186$	−3.30439e38	−	1.84220e38i	−0.865708	−	0.482633i
$187$			1.41034e37i			0.0337300i
$188$	3.34794e38	−	2.06940e38i	0.731298	−	0.452023i
$189$	−2.84809e38			−0.568465
$190$	−1.73763e38	+	3.11682e38i	−0.317063	+	0.568723i
$191$		−	6.06399e38i		−	1.01203i	−0.862526	−	0.506013i	$-0.831119\pi$
$191$		−	6.06399e38i		−	1.01203i	0.862526	−	0.506013i	$-0.168881\pi$
$192$	−3.78485e37	−	4.18973e38i	−0.0578000	−	0.639830i
$193$	5.07300e38			0.709236			0.354618	−	0.935011i	$-0.384611\pi$
$193$	5.07300e38			0.709236			0.354618	+	0.935011i	$0.384611\pi$
$194$	1.21771e38	+	6.78874e37i	0.155925	+	0.0869281i
$195$			4.67359e38i			0.548355i
$196$	3.36913e38	+	5.45070e38i	0.362381	+	0.586272i
$197$	1.53316e38			0.151238			0.0756189	−	0.997137i	$-0.475907\pi$
$197$	1.53316e38			0.151238			0.0756189	+	0.997137i	$0.475907\pi$
$198$	2.08501e37	−	3.73993e37i	0.0188712	−	0.0338497i
$199$		−	1.08591e38i		−	0.0902176i	−0.998982	−	0.0451088i	$-0.985637\pi$
$199$		−	1.08591e38i		−	0.0902176i	0.998982	−	0.0451088i	$-0.0143634\pi$
$200$	−1.65275e37	−	3.66656e38i	−0.0126095	−	0.279736i
$201$	1.44289e39			1.01135
$202$	−1.90035e39	−	1.05944e39i	−1.22422	−	0.682503i
$203$		−	5.70399e38i		−	0.337867i
$204$	5.12641e38	−	3.16869e38i	0.279319	−	0.172650i
$205$	6.59708e38			0.330778
$206$	−6.04232e37	+	1.08382e38i	−0.0278908	+	0.0500283i
$207$		−	2.51852e39i		−	1.07065i
$208$	−1.14833e39	+	2.29730e39i	−0.449771	+	0.899789i
$209$	1.40275e38			0.0506398
$210$	−7.97388e38	−	4.44544e38i	−0.265425	−	0.147975i
$211$			6.11765e38i			0.187838i	0.995580	+	0.0939189i	$0.0299394\pi$
$211$			6.11765e38i			0.187838i	−0.995580	+	0.0939189i	$0.970061\pi$
$212$	9.60702e38	+	1.55426e39i	0.272194	+	0.440365i
$213$	4.11003e39			1.07496
$214$	−2.61466e39	+	4.68997e39i	−0.631512	+	1.13276i
$215$		−	1.83509e39i		−	0.409453i
$216$	−4.94032e39	+	2.22692e38i	−1.01869	+	0.0459189i
$217$	−4.51178e39			−0.860067
$218$	2.14114e39	+	1.19368e39i	0.377471	+	0.210440i
$219$			6.70218e39i			1.09312i
$220$	3.15547e38	−	1.95043e38i	0.0476298	−	0.0294405i
$221$	−3.67938e39			−0.514170
$222$	3.11167e39	−	5.58146e39i	0.402710	−	0.722350i
$223$			7.94706e39i			0.952849i	0.879215	+	0.476424i	$0.158067\pi$
$223$			7.94706e39i			0.952849i	−0.879215	+	0.476424i	$0.841933\pi$
$224$	−2.82728e39	−	4.14440e39i	−0.314161	−	0.460516i
$225$	−1.59637e39			−0.164449
$226$	1.37325e40	+	7.65588e39i	1.31192	+	0.731394i
$227$		−	1.05589e40i		−	0.935796i	−0.883783	−	0.467898i	$-0.845011\pi$
$227$		−	1.05589e40i		−	0.935796i	0.883783	−	0.467898i	$-0.154989\pi$
$228$	−3.15163e39	−	5.09881e39i	−0.259204	−	0.419350i
$229$	5.79914e39			0.442752			0.221376	−	0.975189i	$-0.428945\pi$
$229$	5.79914e39			0.442752			0.221376	+	0.975189i	$0.428945\pi$
$230$	1.06247e40	−	1.90577e40i	0.753255	−	1.35113i
$231$			3.58870e38i			0.0236338i
$232$	−4.45994e38	−	9.89417e39i	−0.0272919	−	0.605458i
$233$	−5.75523e39			−0.327350			−0.163675	−	0.986514i	$-0.552335\pi$
$233$	−5.75523e39			−0.327350			−0.163675	+	0.986514i	$0.552335\pi$
$234$	9.75696e39	+	5.43951e39i	0.515995	+	0.287667i
$235$		−	1.48310e40i		−	0.729488i
$236$	6.13170e38	−	3.79006e38i	0.0280593	−	0.0173437i
$237$	−2.35614e40			−1.00341
$238$	3.49977e39	−	6.27761e39i	0.138750	−	0.248878i
$239$			1.18884e40i			0.438893i	0.975625	+	0.219447i	$0.0704251\pi$
$239$			1.18884e40i			0.438893i	−0.975625	+	0.219447i	$0.929575\pi$
$240$	−1.41791e40	−	7.08762e39i	−0.487594	−	0.243730i
$241$	−2.28994e40			−0.733726			−0.366863	−	0.930275i	$-0.619568\pi$
$241$	−2.28994e40			−0.733726			−0.366863	+	0.930275i	$0.619568\pi$
$242$	2.91203e40	+	1.62346e40i	0.869632	+	0.484820i
$243$			3.50608e40i			0.976146i
$244$	3.24654e40	+	5.25237e40i	0.842935	+	1.36373i
$245$	2.41461e40			0.584821
$246$	−5.39608e39	+	9.67907e39i	−0.121950	+	0.218744i
$247$			3.65957e40i			0.771938i
$248$	−7.82616e40	+	3.52776e39i	−1.54124	+	0.0694736i
$249$	2.23243e40			0.410571
$250$	−5.52189e40	−	3.07846e40i	−0.948654	−	0.528875i
$251$		−	5.78655e40i		−	0.928895i	−0.885601	−	0.464447i	$-0.846253\pi$
$251$		−	5.78655e40i		−	0.928895i	0.885601	−	0.464447i	$-0.153747\pi$
$252$	−1.85613e40	+	1.14730e40i	−0.278484	+	0.172134i
$253$	−8.57703e39			−0.120306
$254$	2.46097e39	−	4.41429e39i	0.0322800	−	0.0579012i
$255$		−	2.27095e40i		−	0.278628i
$256$	−5.22827e40	−	6.96783e40i	−0.600176	−	0.799868i
$257$	1.57494e41			1.69201			0.846003	−	0.533178i	$-0.179002\pi$
$257$	1.57494e41			1.69201			0.846003	+	0.533178i	$0.179002\pi$
$258$	2.69240e40	+	1.50101e40i	0.270773	+	0.150956i
$259$		−	7.62086e40i		−	0.717643i
$260$	5.08840e40	+	8.23219e40i	0.448781	+	0.726054i
$261$	−4.30780e40			−0.355932
$262$	−5.14700e40	+	9.23228e40i	−0.398503	+	0.714804i
$263$		−	3.05475e40i		−	0.221681i	−0.993838	−	0.110840i	$-0.964646\pi$
$263$		−	3.05475e40i		−	0.221681i	0.993838	−	0.110840i	$-0.0353542\pi$
$264$	2.80600e38	+	6.22498e39i	0.00190906	+	0.0423517i
$265$	6.88520e40			0.439275
$266$	−6.24381e40	−	3.48093e40i	−0.373647	−	0.208309i
$267$		−	3.13867e40i		−	0.176220i
$268$	2.54154e41	−	1.57095e41i	1.33908	−	0.827698i
$269$	7.00941e40			0.346651			0.173325	−	0.984865i	$-0.444549\pi$
$269$	7.00941e40			0.346651			0.173325	+	0.984865i	$0.444549\pi$
$270$	−9.07407e40	+	1.62763e41i	−0.421326	+	0.755741i
$271$		−	6.84353e40i		−	0.298402i	−0.988807	−	0.149201i	$-0.952330\pi$
$271$		−	6.84353e40i		−	0.298402i	0.988807	−	0.149201i	$-0.0476702\pi$
$272$	5.57988e40	−	1.11628e41i	0.228536	−	0.457197i
$273$	−9.36242e40			−0.360266
$274$	−3.65705e41	−	2.03881e41i	−1.32243	−	0.737253i
$275$			5.43660e39i			0.0184787i
$276$	1.92705e41	+	3.11765e41i	0.615798	+	0.996260i
$277$	−5.45252e40			−0.163848			−0.0819240	−	0.996639i	$-0.526106\pi$
$277$	−5.45252e40			−0.163848			−0.0819240	+	0.996639i	$0.526106\pi$
$278$	1.22917e41	−	2.20479e41i	0.347417	−	0.623169i
$279$			3.40741e41i			0.906053i
$280$	−1.88854e41	+	8.51288e39i	−0.472542	+	0.0213005i
$281$	−5.70960e41			−1.34461			−0.672307	−	0.740272i	$-0.734697\pi$
$281$	−5.70960e41			−1.34461			−0.672307	+	0.740272i	$0.734697\pi$
$282$	2.17597e41	+	1.21311e41i	0.482412	+	0.268945i
$283$			5.84403e41i			1.21995i	0.792419	+	0.609977i	$0.208821\pi$
$283$			5.84403e41i			1.21995i	−0.792419	+	0.609977i	$0.791179\pi$
$284$	7.23953e41	−	4.47482e41i	1.42331	−	0.879760i
$285$	−2.25872e41			−0.418312
$286$	1.85248e40	−	3.32282e40i	0.0323244	−	0.0579809i
$287$			1.32157e41i			0.217319i
$288$	−3.12996e41	+	2.13524e41i	−0.485139	+	0.330959i
$289$	−5.05541e41			−0.738743
$290$	−3.25973e41	−	1.81730e41i	−0.449175	−	0.250415i
$291$			8.82459e40i			0.114687i
$292$	7.29705e41	+	1.18054e42i	0.894620	+	1.44735i
$293$	4.05544e41			0.469125			0.234563	−	0.972101i	$-0.424634\pi$
$293$	4.05544e41			0.469125			0.234563	+	0.972101i	$0.424634\pi$
$294$	−1.97503e41	+	3.54265e41i	−0.215610	+	0.386744i
$295$		−	2.71628e40i		−	0.0279898i
$296$	−5.95875e40	−	1.32192e42i	−0.0579690	−	1.28602i
$297$	7.32527e40			0.0672921
$298$	1.68830e41	+	9.41231e40i	0.146479	+	0.0816619i
$299$		−	2.23763e42i		−	1.83391i
$300$	1.97614e41	−	1.22147e41i	0.153023	−	0.0945849i
$301$	3.67617e41			0.269008
$302$	7.51274e41	−	1.34758e42i	0.519613	−	0.932041i
$303$		−	1.37716e42i		−	0.900448i
$304$	−1.11027e42	−	5.54984e41i	−0.686403	−	0.343107i
$305$	2.32675e42			1.36035
$306$	−4.74102e41	−	2.64312e41i	−0.262185	−	0.146168i
$307$			3.09454e42i			1.61899i	0.587127	+	0.809495i	$0.300259\pi$
$307$			3.09454e42i			1.61899i	−0.587127	+	0.809495i	$0.699741\pi$
$308$	3.90722e40	+	6.32124e40i	0.0193422	+	0.0312925i
$309$	−7.85433e40			−0.0367972
$310$	−1.43746e42	+	2.57840e42i	−0.637451	+	1.14341i
$311$		−	1.35368e42i		−	0.568317i	−0.958777	−	0.284158i	$-0.908286\pi$
$311$		−	1.35368e42i		−	0.568317i	0.958777	−	0.284158i	$-0.0917141\pi$
$312$	−1.62401e42	+	7.32047e40i	−0.645596	+	0.0291012i
$313$	4.42782e41			0.166700			0.0833501	−	0.996520i	$-0.473438\pi$
$313$	4.42782e41			0.166700			0.0833501	+	0.996520i	$0.473438\pi$
$314$	1.87380e42	+	1.04464e42i	0.668218	+	0.372532i
$315$			8.22249e41i			0.277795i
$316$	−4.15017e42	+	2.56526e42i	−1.32857	+	0.821205i
$317$	2.55541e42			0.775270			0.387635	−	0.921813i	$-0.373292\pi$
$317$	2.55541e42			0.775270			0.387635	+	0.921813i	$0.373292\pi$
$318$	−5.63175e41	+	1.01018e42i	−0.161951	+	0.290494i
$319$			1.46706e41i			0.0399951i
$320$	−3.26923e42	+	2.95330e41i	−0.845075	+	0.0763411i
$321$	−3.39876e42			−0.833173
$322$	3.81775e42	+	2.12840e42i	0.887684	+	0.494884i
$323$		−	1.77823e42i		−	0.392233i
$324$	−1.70409e41	−	2.75693e41i	−0.0356637	−	0.0576980i
$325$	−1.41833e42			−0.281684
$326$	2.55119e42	−	4.57612e42i	0.480887	−	0.862578i
$327$			1.55165e42i			0.277641i
$328$	1.03333e41	+	2.29240e42i	0.0175544	+	0.389435i
$329$	2.97105e42			0.479269
$330$	2.05088e41	+	1.14336e41i	0.0314197	+	0.0175165i
$331$			2.93715e42i			0.427416i	0.976898	+	0.213708i	$0.0685541\pi$
$331$			2.93715e42i			0.427416i	−0.976898	+	0.213708i	$0.931446\pi$
$332$	3.93226e42	−	2.43057e42i	0.543620	−	0.336017i
$333$	−5.75548e42			−0.756013
$334$	6.20162e42	−	1.11240e43i	0.774132	−	1.38858i
$335$		−	1.12588e43i		−	1.33576i
$336$	1.41984e42	−	2.84045e42i	0.160129	−	0.320346i
$337$	−6.07483e42			−0.651368			−0.325684	−	0.945479i	$-0.605594\pi$
$337$	−6.07483e42			−0.651368			−0.325684	+	0.945479i	$0.605594\pi$
$338$	1.02072e41	+	5.69052e40i	0.0104069	+	0.00580187i
$339$			9.95177e42i			0.964951i
$340$	−2.47251e42	−	4.00012e42i	−0.228033	−	0.368919i
$341$	1.16043e42			0.101811
$342$	−2.62889e42	+	4.71549e42i	−0.219446	+	0.393626i
$343$			1.18552e43i			0.941693i
$344$	6.37671e42	−	2.87440e41i	0.482063	−	0.0217297i
$345$	1.38109e43			0.993793
$346$	7.57201e42	+	4.22140e42i	0.518702	+	0.289176i
$347$		−	8.92154e42i		−	0.581887i	−0.956740	−	0.290944i	$-0.906031\pi$
$347$		−	8.92154e42i		−	0.581887i	0.956740	−	0.290944i	$-0.0939692\pi$
$348$	5.33259e42	−	3.29613e42i	0.331200	−	0.204718i
$349$	−1.89322e43			−1.11988			−0.559938	−	0.828535i	$-0.689175\pi$
$349$	−1.89322e43			−1.11988			−0.559938	+	0.828535i	$0.689175\pi$
$350$	1.34910e42	−	2.41990e42i	0.0760128	−	0.136346i
$351$			1.91106e43i			1.02578i
$352$	7.27175e41	+	1.06594e42i	0.0371889	+	0.0545137i
$353$	−2.28963e43			−1.11582			−0.557912	−	0.829900i	$-0.688397\pi$
$353$	−2.28963e43			−1.11582			−0.557912	+	0.829900i	$0.688397\pi$
$354$	3.98525e41	+	2.22178e41i	0.0185098	+	0.0103192i
$355$		−	3.20704e43i		−	1.41978i
$356$	−3.41725e42	−	5.52855e42i	−0.144221	−	0.233325i
$357$	4.54930e42			0.183057
$358$	−1.52084e43	+	2.72797e43i	−0.583544	+	1.04671i
$359$		−	1.32335e42i		−	0.0484248i	−0.999707	−	0.0242124i	$-0.992292\pi$
$359$		−	1.32335e42i		−	0.0484248i	0.999707	−	0.0242124i	$-0.00770779\pi$
$360$	6.42915e41	+	1.42628e43i	0.0224394	+	0.497808i
$361$	1.23481e43			0.411129
$362$	−4.07167e43	−	2.26996e43i	−1.29338	−	0.721060i
$363$			2.11031e43i			0.639638i
$364$	−1.64912e43	+	1.01934e43i	−0.477013	+	0.294846i
$365$	5.22968e43			1.44376
$366$	−1.90316e43	+	3.41374e43i	−0.501531	+	0.899606i
$367$			4.47029e41i			0.0112464i	0.999984	+	0.00562319i	$0.00178993\pi$
$367$			4.47029e41i			0.0112464i	−0.999984	+	0.00562319i	$0.998210\pi$
$368$	6.78872e43	+	3.39343e43i	1.63070	+	0.815128i
$369$	9.98084e42			0.228938
$370$	−4.35519e43	−	2.42802e43i	−0.954065	−	0.531891i
$371$			1.37929e43i			0.288601i
$372$	−2.60719e43	−	4.21801e43i	−0.521127	−	0.843097i
$373$	5.76669e43			1.10123			0.550613	−	0.834761i	$-0.314394\pi$
$373$	5.76669e43			1.10123			0.550613	+	0.834761i	$0.314394\pi$
$374$	−9.00139e41	+	1.61460e42i	−0.0164245	+	0.0294610i
$375$		−	4.00164e43i		−	0.697761i
$376$	5.15360e43	−	2.32306e42i	0.858850	−	0.0387139i
$377$	−3.82736e43			−0.609672
$378$	−3.26058e43	−	1.81777e43i	−0.496517	−	0.276808i
$379$		−	1.17062e44i		−	1.70431i	−0.523288	−	0.852156i	$-0.675295\pi$
$379$		−	1.17062e44i		−	1.70431i	0.523288	−	0.852156i	$-0.324705\pi$
$380$	−3.97858e43	+	2.45920e43i	−0.553869	+	0.342352i
$381$	3.19898e42			0.0425880
$382$	3.87030e43	−	6.94223e43i	0.492796	−	0.883938i
$383$			2.28376e43i			0.278145i	0.990282	+	0.139072i	$0.0444121\pi$
$383$			2.28376e43i			0.278145i	−0.990282	+	0.139072i	$0.955588\pi$
$384$	2.24076e43	−	5.03809e43i	0.261075	−	0.586996i
$385$	2.80024e42			0.0312150
$386$	5.80772e43	+	3.23781e43i	0.619471	+	0.345356i
$387$		−	2.77634e43i		−	0.283391i
$388$	9.60784e42	+	1.55439e43i	0.0938613	+	0.151852i
$389$	9.45576e41			0.00884205			0.00442103	−	0.999990i	$-0.498593\pi$
$389$	9.45576e41			0.00884205			0.00442103	+	0.999990i	$0.498593\pi$
$390$	−2.98288e43	+	5.35046e43i	−0.267016	+	0.478953i
$391$			1.08729e44i			0.931838i
$392$	3.78211e42	+	8.39045e43i	0.0310364	+	0.688528i
$393$	−6.69051e43			−0.525758
$394$	1.75520e43	+	9.78526e42i	0.132096	+	0.0736438i
$395$			1.83848e44i			1.32529i
$396$	4.77396e42	−	2.95084e42i	0.0329656	−	0.0203764i
$397$	−1.93544e44			−1.28039			−0.640195	−	0.768213i	$-0.721146\pi$
$397$	−1.93544e44			−1.28039			−0.640195	+	0.768213i	$0.721146\pi$
$398$	6.93073e42	−	1.24318e43i	0.0439306	−	0.0787992i
$399$		−	4.52481e43i		−	0.274828i
$400$	2.15094e43	−	4.30307e43i	0.125201	−	0.250472i
$401$	−1.52086e44			−0.848466			−0.424233	−	0.905553i	$-0.639456\pi$
$401$	−1.52086e44			−0.848466			−0.424233	+	0.905553i	$0.639456\pi$
$402$	1.65186e44	+	9.20912e43i	0.883344	+	0.492465i
$403$			3.02739e44i			1.55197i
$404$	−1.49939e44	−	2.42576e44i	−0.736938	−	1.19224i
$405$	−1.22129e43			−0.0575552
$406$	3.64053e43	−	6.53009e43i	0.164521	−	0.295105i
$407$			1.96008e43i			0.0849511i
$408$	7.89126e43	−	3.55710e42i	0.328037	−	0.0147868i
$409$	1.14576e44			0.456876			0.228438	−	0.973558i	$-0.426638\pi$
$409$	1.14576e44			0.456876			0.228438	+	0.973558i	$0.426638\pi$
$410$	7.55253e43	+	4.21054e43i	0.288913	+	0.161069i
$411$		−	2.65022e44i		−	0.972681i
$412$	−1.38348e43	+	8.55146e42i	−0.0487216	+	0.0301153i
$413$	5.44142e42			0.0183891
$414$	1.60742e44	−	2.88327e44i	0.521344	−	0.935146i
$415$		−	1.74195e44i		−	0.542274i
$416$	−2.78088e44	+	1.89710e44i	−0.830990	+	0.566896i
$417$	1.59778e44			0.458358
$418$	1.60590e43	+	8.95292e42i	0.0442306	+	0.0246586i
$419$		−	5.13503e44i		−	1.35801i	−0.734131	−	0.679007i	$-0.762410\pi$
$419$		−	5.13503e44i		−	1.35801i	0.734131	−	0.679007i	$-0.237590\pi$
$420$	−6.29146e43	−	1.01785e44i	−0.159777	−	0.258492i
$421$	3.75101e44			0.914857			0.457428	−	0.889246i	$-0.348771\pi$
$421$	3.75101e44			0.914857			0.457428	+	0.889246i	$0.348771\pi$
$422$	−3.90455e43	+	7.00367e43i	−0.0914658	+	0.164064i
$423$		−	2.24381e44i		−	0.504894i
$424$	1.07846e43	+	2.39252e44i	0.0233123	+	0.517173i
$425$	6.89185e43			0.143128
$426$	4.70528e44	+	2.62320e44i	0.938906	+	0.523441i
$427$			4.66108e44i			0.893744i
$428$	−5.98668e44	+	3.70043e44i	−1.10317	+	0.681880i
$429$	2.40801e43			0.0426465
$430$	1.17123e44	−	2.10087e44i	0.199379	−	0.357631i
$431$			5.86754e44i			0.960158i	0.877225	+	0.480079i	$0.159392\pi$
$431$			5.86754e44i			0.960158i	−0.877225	+	0.480079i	$0.840608\pi$
$432$	−5.79796e44	−	2.89818e44i	−0.912118	−	0.455934i
$433$	−3.06479e44			−0.463561			−0.231781	−	0.972768i	$-0.574455\pi$
$433$	−3.06479e44			−0.463561			−0.231781	+	0.972768i	$0.574455\pi$
$434$	−5.16522e44	−	2.87961e44i	−0.751213	−	0.418802i
$435$		−	2.36228e44i		−	0.330381i
$436$	1.68937e44	+	2.73313e44i	0.227225	+	0.367612i
$437$	1.08144e45			1.39900
$438$	−4.27762e44	+	7.67285e44i	−0.532282	+	0.954766i
$439$		−	1.33042e45i		−	1.59255i	−0.604937	−	0.796273i	$-0.706802\pi$
$439$		−	1.33042e45i		−	1.59255i	0.604937	−	0.796273i	$-0.293198\pi$
$440$	4.85732e43	−	2.18951e42i	0.0559373	−	0.00252145i
$441$	3.65310e44			0.404767
$442$	−4.21226e44	−	2.34834e44i	−0.449094	−	0.250370i
$443$			1.40788e45i			1.44445i	0.691656	+	0.722227i	$0.256881\pi$
$443$			1.40788e45i			1.44445i	−0.691656	+	0.722227i	$0.743119\pi$
$444$	7.12465e44	−	4.40382e44i	0.703483	−	0.434830i
$445$	−2.44909e44			−0.232748
$446$	−5.07215e44	+	9.09803e44i	−0.463981	+	0.832252i
$447$			1.22349e44i			0.107739i
$448$	−5.91624e43	−	6.54911e44i	−0.0501556	−	0.555209i
$449$	−2.39263e45			−1.95294			−0.976468	−	0.215663i	$-0.930809\pi$
$449$	−2.39263e45			−1.95294			−0.976468	+	0.215663i	$0.930809\pi$
$450$	−1.82758e44	−	1.01887e44i	−0.143636	−	0.0800770i
$451$		−	3.39907e43i		−	0.0257252i
$452$	1.08351e45	+	1.75293e45i	0.789729	+	1.27765i
$453$	9.76571e44			0.685542
$454$	6.73917e44	−	1.20882e45i	0.455677	−	0.817357i
$455$			7.30545e44i			0.475832i
$456$	−3.53795e43	−	7.84877e44i	−0.0221998	−	0.492492i
$457$	−7.62339e44			−0.460864			−0.230432	−	0.973088i	$-0.574014\pi$
$457$	−7.62339e44			−0.460864			−0.230432	+	0.973088i	$0.574014\pi$
$458$	6.63902e44	+	3.70126e44i	0.386715	+	0.215594i
$459$		−	9.28608e44i		−	0.521215i
$460$	2.43269e45	−	1.50367e45i	1.31584	−	0.813334i
$461$	−4.08079e44			−0.212730			−0.106365	−	0.994327i	$-0.533921\pi$
$461$	−4.08079e44			−0.212730			−0.106365	+	0.994327i	$0.533921\pi$
$462$	−2.29046e43	+	4.10844e43i	−0.0115082	+	0.0206426i
$463$		−	4.89009e44i		−	0.236832i	−0.992964	−	0.118416i	$-0.962218\pi$
$463$		−	4.89009e44i		−	0.236832i	0.992964	−	0.118416i	$-0.0377816\pi$
$464$	5.80430e44	−	1.16118e45i	0.270984	−	0.542118i
$465$	−1.86853e45			−0.841010
$466$	−6.58876e44	−	3.67323e44i	−0.285919	−	0.159400i
$467$			1.85973e44i			0.0778150i	0.999243	+	0.0389075i	$0.0123878\pi$
$467$			1.85973e44i			0.0778150i	−0.999243	+	0.0389075i	$0.987612\pi$
$468$	7.69833e44	+	1.24546e45i	0.310611	+	0.502517i
$469$	2.25543e45			0.877588
$470$	9.46581e44	−	1.69790e45i	0.355217	−	0.637160i
$471$			1.35792e45i			0.491493i
$472$	9.43873e43	−	4.25464e42i	0.0329533	−	0.00148542i
$473$	−9.45509e43			−0.0318439
$474$	−2.69738e45	−	1.50379e45i	−0.876415	−	0.488602i
$475$		−	6.85474e44i		−	0.214882i
$476$	8.01328e44	−	4.95309e44i	0.242377	−	0.149816i
$477$	1.04167e45			0.304032
$478$	−7.58768e44	+	1.36102e45i	−0.213715	+	0.383345i
$479$		−	7.30451e44i		−	0.198558i	−0.995060	−	0.0992790i	$-0.968346\pi$
$479$		−	7.30451e44i		−	0.198558i	0.995060	−	0.0992790i	$-0.0316536\pi$
$480$	−1.17091e45	−	1.71638e45i	−0.307200	−	0.450312i
$481$	−5.11358e45			−1.29497
$482$	−2.62159e45	−	1.46154e45i	−0.640862	−	0.357281i
$483$			2.76668e45i			0.652916i
$484$	2.29762e45	+	3.71717e45i	0.523488	+	0.846918i
$485$	6.88579e44			0.151476
$486$	−2.23773e45	+	4.01386e45i	−0.475325	+	0.852601i
$487$			5.74351e45i			1.17811i	0.808094	+	0.589054i	$0.200499\pi$
$487$			5.74351e45i			1.17811i	−0.808094	+	0.589054i	$0.799501\pi$
$488$	3.64450e44	+	8.08515e45i	0.0721939	+	1.60159i
$489$	3.31625e45			0.634450
$490$	2.76431e45	+	1.54110e45i	0.510803	+	0.284773i
$491$		−	5.84413e45i		−	1.04312i	−0.853215	−	0.521560i	$-0.825350\pi$
$491$		−	5.84413e45i		−	1.04312i	0.853215	−	0.521560i	$-0.174650\pi$
$492$	−1.23552e45	+	7.63686e44i	−0.213031	+	0.131677i
$493$	1.85976e45			0.309784
$494$	−2.33570e45	+	4.18958e45i	−0.375888	+	0.674237i
$495$		−	2.11482e44i		−	0.0328840i
$496$	−9.18478e45	−	4.59112e45i	−1.38000	−	0.689812i
$497$	6.42454e45			0.932788
$498$	2.55575e45	+	1.42483e45i	0.358607	+	0.199924i
$499$		−	8.01707e45i		−	1.08719i	−0.839347	−	0.543596i	$-0.817062\pi$
$499$		−	8.01707e45i		−	1.08719i	0.839347	−	0.543596i	$-0.182938\pi$
$500$	−4.35682e45	−	7.04861e45i	−0.571057	−	0.923876i
$501$	8.06140e45			1.02134
$502$	3.69322e45	−	6.62461e45i	0.452316	−	0.811329i
$503$		−	1.11697e46i		−	1.32247i	−0.750178	−	0.661236i	$-0.770032\pi$
$503$		−	1.11697e46i		−	1.32247i	0.750178	−	0.661236i	$-0.229968\pi$
$504$	−2.85721e45	+	1.28793e44i	−0.327057	+	0.0147425i
$505$	−1.07459e46			−1.18929
$506$	−9.81924e44	−	5.47423e44i	−0.105080	−	0.0585820i
$507$			7.39703e43i			0.00765459i
$508$	5.63478e44	−	3.48291e44i	0.0563889	−	0.0348546i
$509$	1.52847e46			1.47929			0.739647	−	0.672995i	$-0.234992\pi$
$509$	1.52847e46			1.47929			0.739647	+	0.672995i	$0.234992\pi$
$510$	1.44942e45	−	2.59985e45i	0.135675	−	0.243363i
$511$			1.04764e46i			0.948544i
$512$	−1.53831e45	−	1.13139e46i	−0.134727	−	0.990883i
$513$	−9.23608e45			−0.782515
$514$	1.80304e46	+	1.00520e46i	1.47786	+	0.823906i
$515$			6.12870e44i			0.0486010i
$516$	2.12433e45	+	3.43681e45i	0.162996	+	0.263700i
$517$	−7.64151e44			−0.0567336
$518$	4.86396e45	−	8.72459e45i	0.349449	−	0.626814i
$519$			5.48734e45i			0.381520i
$520$	5.71213e44	+	1.26721e46i	0.0384362	+	0.852690i
$521$	−6.48428e45			−0.422300			−0.211150	−	0.977454i	$-0.567721\pi$
$521$	−6.48428e45			−0.422300			−0.211150	+	0.977454i	$0.567721\pi$
$522$	−4.93169e45	−	2.74942e45i	−0.310883	−	0.173318i
$523$			1.86380e46i			1.13729i	0.822583	+	0.568646i	$0.192532\pi$
$523$			1.86380e46i			1.13729i	−0.822583	+	0.568646i	$0.807468\pi$
$524$	−1.17849e46	+	7.28434e45i	−0.696134	+	0.430287i
$525$	1.75367e45			0.100286
$526$	1.94967e45	−	3.49717e45i	0.107945	−	0.193624i
$527$		−	1.47105e46i		−	0.788580i
$528$	−3.65181e44	+	7.30562e44i	−0.0189553	+	0.0379211i
$529$	−4.62289e46			−2.32363
$530$	7.88238e45	+	4.39443e45i	0.383679	+	0.213901i
$531$		−	4.10950e44i		−	0.0193724i
$532$	−4.92642e45	−	7.97014e45i	−0.224923	−	0.363888i
$533$	8.86770e45			0.392146
$534$	2.00324e45	−	3.59324e45i	0.0858086	−	0.153917i
$535$			2.65204e46i			1.10044i
$536$	3.91228e46	−	1.76352e45i	1.57264	−	0.0708889i
$537$	−1.97693e46			−0.769888
$538$	8.02457e45	+	4.47370e45i	0.302777	+	0.168798i
$539$		−	1.24410e45i		−	0.0454825i
$540$	−2.07765e46	+	1.28422e46i	−0.736002	+	0.454930i
$541$	5.83524e45			0.200311			0.100156	−	0.994972i	$-0.468066\pi$
$541$	5.83524e45			0.200311			0.100156	+	0.994972i	$0.468066\pi$
$542$	4.36783e45	−	7.83467e45i	0.145304	−	0.260635i
$543$		−	2.95068e46i		−	0.951318i
$544$	1.35126e46	−	9.21822e45i	0.422239	−	0.288049i
$545$	1.21075e46			0.366702
$546$	−1.07184e46	−	5.97549e45i	−0.314669	−	0.175428i
$547$			5.22326e46i			1.48647i	0.669029	+	0.743236i	$0.266710\pi$
$547$			5.22326e46i			1.48647i	−0.669029	+	0.743236i	$0.733290\pi$
$548$	−2.88544e46	−	4.66817e46i	−0.796055	−	1.28789i
$549$	3.52017e46			0.941530
$550$	−3.46987e44	+	6.22398e44i	−0.00899803	+	0.0161400i
$551$		−	1.84975e46i		−	0.465088i
$552$	2.16326e45	+	4.79910e46i	0.0527406	+	1.17003i
$553$	−3.68297e46			−0.870704
$554$	−6.24220e45	−	3.48003e45i	−0.143111	−	0.0797843i
$555$		−	3.15615e46i		−	0.701741i
$556$	2.81438e46	−	1.73960e46i	0.606893	−	0.375126i
$557$	9.34319e46			1.95415			0.977073	−	0.212906i	$-0.0682929\pi$
$557$	9.34319e46			1.95415			0.977073	+	0.212906i	$0.0682929\pi$
$558$	−2.17476e46	+	3.90091e46i	−0.441194	+	0.791378i
$559$		−	2.46670e46i		−	0.485418i
$560$	−2.21639e46	−	1.10789e46i	−0.423107	−	0.211495i
$561$	−1.17008e45			−0.0216694
$562$	−6.53651e46	−	3.64411e46i	−1.17443	−	0.654747i
$563$		−	6.62861e46i		−	1.15553i	−0.816204	−	0.577763i	$-0.803926\pi$
$563$		−	6.62861e46i		−	1.15553i	0.816204	−	0.577763i	$-0.196074\pi$
$564$	1.71686e46	+	2.77760e46i	0.290396	+	0.469812i
$565$	7.76532e46			1.27449
$566$	−3.72991e46	+	6.69042e46i	−0.594045	+	1.06555i
$567$		−	2.44657e45i		−	0.0378134i
$568$	1.11440e47	−	5.02334e45i	1.67156	−	0.0753478i
$569$	−8.92896e46			−1.29985			−0.649923	−	0.760000i	$-0.725199\pi$
$569$	−8.92896e46			−1.29985			−0.649923	+	0.760000i	$0.725199\pi$
$570$	−2.58585e46	−	1.44161e46i	−0.365368	−	0.203693i
$571$		−	1.56228e46i		−	0.214262i	−0.994245	−	0.107131i	$-0.965834\pi$
$571$		−	1.56228e46i		−	0.214262i	0.994245	−	0.107131i	$-0.0341664\pi$
$572$	4.24154e45	−	2.62174e45i	0.0564665	−	0.0349025i
$573$	5.03095e46			0.650161
$574$	−8.43481e45	+	1.51297e46i	−0.105821	+	0.189814i
$575$			4.19130e46i			0.510500i
$576$	−4.94606e46	+	4.46810e45i	−0.584895	+	0.0528373i
$577$	−8.63671e46			−0.991652			−0.495826	−	0.868422i	$-0.665135\pi$
$577$	−8.63671e46			−0.991652			−0.495826	+	0.868422i	$0.665135\pi$
$578$	−5.78758e46	−	3.22658e46i	−0.645244	−	0.359724i
$579$			4.20878e46i			0.455638i
$580$	−2.57195e46	−	4.16099e46i	−0.270388	−	0.437443i
$581$	3.48959e46			0.356271
$582$	−5.63223e45	+	1.01027e46i	−0.0558457	+	0.100172i
$583$		−	3.54751e45i		−	0.0341632i
$584$	8.19150e45	+	1.81725e47i	0.0766205	+	1.69979i
$585$	5.51727e46			0.501273
$586$	4.64279e46	+	2.58836e46i	0.409751	+	0.228436i
$587$			1.78766e47i			1.53263i	0.642463	+	0.766316i	$0.277912\pi$
$587$			1.78766e47i			1.53263i	−0.642463	+	0.766316i	$0.722088\pi$
$588$	−4.52213e46	+	2.79518e46i	−0.376642	+	0.232806i
$589$	−1.46312e47			−1.18392
$590$	1.73365e45	−	3.10968e45i	0.0136294	−	0.0244473i
$591$			1.27197e46i			0.0971606i
$592$	7.75489e46	−	1.55140e47i	0.575581	−	1.15148i
$593$	5.04091e46			0.363563			0.181781	−	0.983339i	$-0.441814\pi$
$593$	5.04091e46			0.363563			0.181781	+	0.983339i	$0.441814\pi$
$594$	8.38619e45	+	4.67530e45i	0.0587753	+	0.0327673i
$595$		−	3.54980e46i		−	0.241777i
$596$	1.33209e46	+	2.15510e46i	0.0881751	+	0.142653i
$597$	9.00917e45			0.0579590
$598$	1.42815e47	−	2.56170e47i	0.893006	−	1.60180i
$599$			1.86805e45i			0.0113535i	0.999984	+	0.00567677i	$0.00180698\pi$
$599$			1.86805e45i			0.0113535i	−0.999984	+	0.00567677i	$0.998193\pi$
$600$	3.04193e46	−	1.37120e45i	0.179713	−	0.00810081i
$601$	−3.30892e47			−1.90029			−0.950146	−	0.311804i	$-0.899067\pi$
$601$	−3.30892e47			−1.90029			−0.950146	+	0.311804i	$0.899067\pi$
$602$	4.20859e46	+	2.34629e46i	0.234961	+	0.130991i
$603$		−	1.70336e47i		−	0.924511i
$604$	1.72016e47	−	1.06325e47i	0.907697	−	0.561057i
$605$	1.64667e47			0.844821
$606$	8.78960e46	−	1.57661e47i	0.438465	−	0.786483i
$607$			1.36309e46i			0.0661177i	0.999453	+	0.0330588i	$0.0105249\pi$
$607$			1.36309e46i			0.0661177i	−0.999453	+	0.0330588i	$0.989475\pi$
$608$	−9.16859e46	−	1.34399e47i	−0.432456	−	0.633919i
$609$	4.73227e46			0.217058
$610$	2.66373e47	+	1.48503e47i	1.18818	+	0.662411i
$611$		−	1.99357e47i		−	0.864829i
$612$	−3.74070e46	−	6.05184e46i	−0.157826	−	0.255337i
$613$	−1.74577e47			−0.716406			−0.358203	−	0.933644i	$-0.616610\pi$
$613$	−1.74577e47			−0.716406			−0.358203	+	0.933644i	$0.616610\pi$
$614$	−1.97507e47	+	3.54272e47i	−0.788352	+	1.41408i
$615$			5.47322e46i			0.212503i
$616$	4.38616e44	+	9.73049e45i	0.00165658	+	0.0367504i
$617$	−1.96130e47			−0.720603			−0.360302	−	0.932836i	$-0.617326\pi$
$617$	−1.96130e47			−0.720603			−0.360302	+	0.932836i	$0.617326\pi$
$618$	−8.99186e45	−	5.01297e45i	−0.0321400	−	0.0179180i
$619$			2.85150e47i			0.991590i	0.868440	+	0.495795i	$0.165123\pi$
$619$			2.85150e47i			0.991590i	−0.868440	+	0.495795i	$0.834877\pi$
$620$	−3.29129e47	+	2.03438e47i	−1.11355	+	0.688293i
$621$	5.64736e47			1.85904
$622$	8.63978e46	−	1.54974e47i	0.276736	−	0.496388i
$623$		−	4.90617e46i		−	0.152914i
$624$	−1.90594e47	−	9.52707e46i	−0.578057	−	0.288949i
$625$	−2.17372e47			−0.641568
$626$	5.06910e46	+	2.82602e46i	0.145602	+	0.0811731i
$627$			1.16378e46i			0.0325328i
$628$	1.47844e47	+	2.39187e47i	0.402244	+	0.650765i
$629$	2.48475e47			0.657993
$630$	−5.24794e46	+	9.41334e46i	−0.135269	+	0.242636i
$631$			5.99210e47i			1.50342i	0.659494	+	0.751710i	$0.270770\pi$
$631$			5.99210e47i			1.50342i	−0.659494	+	0.751710i	$0.729230\pi$
$632$	−6.38850e47	+	2.87971e46i	−1.56030	+	0.0703328i
$633$	−5.07547e46			−0.120674
$634$	2.92550e47	+	1.63097e47i	0.677148	+	0.377510i
$635$		−	2.49615e46i		−	0.0562493i
$636$	−1.28948e47	+	7.97039e46i	−0.282907	+	0.174867i
$637$	3.24567e47			0.693321
$638$	−9.36341e45	+	1.67953e46i	−0.0194752	+	0.0349331i
$639$		−	4.85198e47i		−	0.982662i
$640$	−3.93120e47	−	1.74846e47i	−0.775292	−	0.344822i
$641$	−1.67263e47			−0.321228			−0.160614	−	0.987017i	$-0.551347\pi$
$641$	−1.67263e47			−0.321228			−0.160614	+	0.987017i	$0.551347\pi$
$642$	−3.89100e47	−	2.16923e47i	−0.727723	−	0.405706i
$643$		−	7.59156e47i		−	1.38275i	−0.722495	−	0.691376i	$-0.757005\pi$
$643$		−	7.59156e47i		−	1.38275i	0.722495	−	0.691376i	$-0.242995\pi$
$644$	3.01224e47	+	4.87331e47i	0.534355	+	0.864498i
$645$	1.52247e47			0.263047
$646$	1.13494e47	−	2.03577e47i	0.190994	−	0.342590i
$647$		−	3.30834e47i		−	0.542298i	−0.962537	−	0.271149i	$-0.912596\pi$
$647$		−	3.30834e47i		−	0.542298i	0.962537	−	0.271149i	$-0.0874035\pi$
$648$	−1.91297e45	−	4.24384e46i	−0.00305445	−	0.0677616i
$649$	−1.39953e45			−0.00217682
$650$	−1.62375e47	−	9.05242e46i	−0.246032	−	0.137163i
$651$		−	3.74316e47i		−	0.552538i
$652$	5.84135e47	−	3.61060e47i	0.840048	−	0.519242i
$653$	6.86204e47			0.961455			0.480727	−	0.876870i	$-0.340373\pi$
$653$	6.86204e47			0.961455			0.480727	+	0.876870i	$0.340373\pi$
$654$	−9.90332e46	+	1.77638e47i	−0.135194	+	0.242501i
$655$			5.22058e47i			0.694411i
$656$	−1.34481e47	+	2.69036e47i	−0.174299	+	0.348695i
$657$	7.91207e47			0.999261
$658$	3.40134e47	+	1.89625e47i	0.418610	+	0.233375i
$659$			4.54026e47i			0.544538i	0.962221	+	0.272269i	$0.0877741\pi$
$659$			4.54026e47i			0.544538i	−0.962221	+	0.272269i	$0.912226\pi$
$660$	1.61816e46	+	2.61791e46i	0.0189136	+	0.0305991i
$661$	−1.17028e48			−1.33311			−0.666555	−	0.745455i	$-0.732232\pi$
$661$	−1.17028e48			−1.33311			−0.666555	+	0.745455i	$0.732232\pi$
$662$	−1.87462e47	+	3.36254e47i	−0.208126	+	0.373320i
$663$		−	3.05257e47i		−	0.330321i
$664$	6.05306e47	−	2.72851e46i	0.638437	−	0.0287785i
$665$	−3.53069e47			−0.362987
$666$	−6.58904e47	−	3.67339e47i	−0.660329	−	0.368133i
$667$			1.13102e48i			1.10492i
$668$	1.41996e48	−	8.77690e47i	1.35231	−	0.835875i
$669$	−6.59322e47			−0.612144
$670$	7.18584e47	−	1.28894e48i	0.650438	−	1.16670i
$671$		−	1.19883e47i		−	0.105797i
$672$	3.43837e47	−	2.34563e47i	0.295852	−	0.201828i
$673$	−1.22899e48			−1.03108			−0.515540	−	0.856866i	$-0.672408\pi$
$673$	−1.22899e48			−1.03108			−0.515540	+	0.856866i	$0.672408\pi$
$674$	−6.95465e47	−	3.87722e47i	−0.568927	−	0.317177i
$675$		−	3.57961e47i		−	0.285543i
$676$	8.05357e45	+	1.30293e46i	0.00626462	+	0.0101351i
$677$	−1.23253e47			−0.0934955			−0.0467477	−	0.998907i	$-0.514886\pi$
$677$	−1.23253e47			−0.0934955			−0.0467477	+	0.998907i	$0.514886\pi$
$678$	−6.35164e47	+	1.13931e48i	−0.469874	+	0.842822i
$679$			1.37940e47i			0.0995189i
$680$	−2.77559e46	−	6.15751e47i	−0.0195300	−	0.433265i
$681$	8.76015e47			0.601189
$682$	1.32849e47	+	7.40634e46i	0.0889250	+	0.0495757i
$683$			1.80253e48i			1.17687i	0.808543	+	0.588437i	$0.200257\pi$
$683$			1.80253e48i			1.17687i	−0.808543	+	0.588437i	$0.799743\pi$
$684$	−6.01926e47	+	3.72056e47i	−0.383344	+	0.236949i
$685$	−2.06795e48			−1.28470
$686$	−7.56650e47	+	1.35722e48i	−0.458549	+	0.822508i
$687$			4.81121e47i			0.284440i
$688$	7.48370e47	+	3.74082e47i	0.431631	+	0.215756i
$689$	9.25498e47			0.520773
$690$	1.58111e48	+	8.81468e47i	0.868014	+	0.483918i
$691$			7.77101e47i			0.416246i	0.978103	+	0.208123i	$0.0667355\pi$
$691$			7.77101e47i			0.416246i	−0.978103	+	0.208123i	$0.933265\pi$
$692$	5.97438e47	+	9.66556e47i	0.312241	+	0.505154i
$693$	4.23653e46			0.0216046
$694$	5.69411e47	−	1.02136e48i	0.283344	−	0.508241i
$695$		−	1.24674e48i		−	0.605390i
$696$	8.20863e47	−	3.70016e46i	0.388968	−	0.0175333i
$697$	−4.30891e47			−0.199256
$698$	−2.16742e48	−	1.20834e48i	−0.978139	−	0.545313i
$699$		−	4.77479e47i		−	0.210301i
$700$	3.08897e47	−	1.90933e47i	0.132785	−	0.0820754i
$701$	−1.17801e48			−0.494244			−0.247122	−	0.968984i	$-0.579485\pi$
$701$	−1.17801e48			−0.494244			−0.247122	+	0.968984i	$0.579485\pi$
$702$	−1.21972e48	+	2.18784e48i	−0.499494	+	0.895952i
$703$		−	2.47137e48i		−	0.987864i
$704$	1.52165e46	+	1.68443e47i	0.00593718	+	0.0657230i
$705$	1.23045e48			0.468649
$706$	−2.62124e48	−	1.46134e48i	−0.974600	−	0.543340i
$707$		−	2.15268e48i		−	0.781358i
$708$	3.14440e46	+	5.08712e46i	0.0111422	+	0.0180263i
$709$	2.19394e48			0.758993			0.379497	−	0.925193i	$-0.376097\pi$
$709$	2.19394e48			0.758993			0.379497	+	0.925193i	$0.376097\pi$
$710$	2.04687e48	−	3.67151e48i	0.691350	−	1.24009i
$711$			2.78147e48i			0.917258i
$712$	−3.83613e46	−	8.51029e47i	−0.0123519	−	0.274021i
$713$	8.94622e48			2.81266
$714$	5.20818e47	+	2.90356e47i	0.159888	+	0.0891377i
$715$		−	1.87896e47i		−	0.0563267i
$716$	−3.48221e48	+	2.15239e48i	−1.01938	+	0.630086i
$717$	−9.86311e47			−0.281961
$718$	8.44615e46	−	1.51500e47i	0.0235800	−	0.0422959i
$719$		−	7.14040e48i		−	1.94685i	−0.229014	−	0.973423i	$-0.573550\pi$
$719$		−	7.14040e48i		−	1.94685i	0.229014	−	0.973423i	$-0.426450\pi$
$720$	−8.36709e47	+	1.67388e48i	−0.222803	+	0.445730i
$721$	−1.22774e47			−0.0319305
$722$	1.41365e48	+	7.88109e47i	0.359094	+	0.200195i
$723$		−	1.89983e48i		−	0.471372i
$724$	−3.21258e48	−	5.19742e48i	−0.778571	−	1.25960i
$725$	7.16903e47			0.169713
$726$	−1.34689e48	+	2.41595e48i	−0.311466	+	0.558682i
$727$			6.95703e48i			1.57159i	0.618488	+	0.785794i	$0.287745\pi$
$727$			6.95703e48i			1.57159i	−0.618488	+	0.785794i	$0.712255\pi$
$728$	−2.53855e48	+	1.14429e47i	−0.560212	+	0.0252524i
$729$	−3.22342e48			−0.694942
$730$	5.98709e48	+	3.33780e48i	1.26103	+	0.703027i
$731$			1.19860e48i			0.246649i
$732$	−4.35759e48	+	2.69347e48i	−0.876109	+	0.541532i
$733$	−4.98745e48			−0.979740			−0.489870	−	0.871796i	$-0.662956\pi$
$733$	−4.98745e48			−0.979740			−0.489870	+	0.871796i	$0.662956\pi$
$734$	−2.85313e46	+	5.11772e46i	−0.00547631	+	0.00982298i
$735$			2.00326e48i			0.375710i
$736$	5.60610e48	+	8.21775e48i	1.02740	+	1.50602i
$737$	−5.80095e47			−0.103885
$738$	1.14263e48	+	6.37019e47i	0.199963	+	0.111479i
$739$			2.78662e48i			0.476565i	0.971196	+	0.238282i	$0.0765844\pi$
$739$			2.78662e48i			0.476565i	−0.971196	+	0.238282i	$0.923416\pi$
$740$	−3.43628e48	−	5.55934e48i	−0.574314	−	0.929145i
$741$	−3.03614e48			−0.495920
$742$	−8.80319e47	+	1.57905e48i	−0.140532	+	0.252074i
$743$			4.04892e48i			0.631728i	0.948805	+	0.315864i	$0.102294\pi$
$743$			4.04892e48i			0.631728i	−0.948805	+	0.315864i	$0.897706\pi$
$744$	−2.92678e47	−	6.49292e48i	−0.0446323	−	0.990148i
$745$	9.54686e47			0.142300
$746$	6.60187e48	+	3.68055e48i	0.961849	+	0.536231i
$747$		−	2.63543e48i		−	0.375319i
$748$	−2.06101e47	+	1.27393e47i	−0.0286915	+	0.0177345i
$749$	−5.31273e48			−0.722981
$750$	2.55402e48	−	4.58120e48i	0.339768	−	0.609449i
$751$			2.00455e48i			0.260698i	0.991468	+	0.130349i	$0.0416098\pi$
$751$			2.00455e48i			0.260698i	−0.991468	+	0.130349i	$0.958390\pi$
$752$	6.04826e48	+	3.02330e48i	0.769001	+	0.384395i
$753$	4.80077e48			0.596755
$754$	−4.38167e48	−	2.44279e48i	−0.532509	−	0.296874i
$755$		−	7.62014e48i		−	0.905450i
$756$	−2.57262e48	−	4.16208e48i	−0.298886	−	0.483548i
$757$	−7.07325e48			−0.803506			−0.401753	−	0.915748i	$-0.631599\pi$
$757$	−7.07325e48			−0.803506			−0.401753	+	0.915748i	$0.631599\pi$
$758$	7.47139e48	−	1.34016e49i	0.829898	−	1.48861i
$759$		−	7.11587e47i		−	0.0772891i
$760$	−6.12436e48	+	2.76064e47i	−0.650473	+	0.0293210i
$761$	2.19853e48			0.228346			0.114173	−	0.993461i	$-0.463578\pi$
$761$	2.19853e48			0.228346			0.114173	+	0.993461i	$0.463578\pi$
$762$	3.66228e47	+	2.04173e47i	0.0371978	+	0.0207378i
$763$			2.42545e48i			0.240921i
$764$	8.86166e48	−	5.47748e48i	0.860851	−	0.532101i
$765$	−2.68090e48			−0.254705
$766$	−1.45759e48	+	2.61451e48i	−0.135440	+	0.242942i
$767$		−	3.65118e47i		−	0.0331827i
$768$	5.78081e48	−	4.33760e48i	0.513864	−	0.385575i
$769$	7.00757e48			0.609284			0.304642	−	0.952467i	$-0.401463\pi$
$769$	7.00757e48			0.609284			0.304642	+	0.952467i	$0.401463\pi$
$770$	3.20580e47	+	1.78723e47i	0.0272643	+	0.0151998i
$771$			1.30664e49i			1.08701i
$772$	4.58234e48	+	7.41347e48i	0.372901	+	0.603291i
$773$	−1.07194e49			−0.853331			−0.426665	−	0.904410i	$-0.640312\pi$
$773$	−1.07194e49			−0.853331			−0.426665	+	0.904410i	$0.640312\pi$
$774$	1.77198e48	−	3.17844e48i	0.137995	−	0.247524i
$775$		−	5.67061e48i		−	0.432017i
$776$	1.07855e47	+	2.39272e48i	0.00803883	+	0.178338i
$777$	6.32259e48			0.461039
$778$	1.08252e47	+	6.03507e46i	0.00772296	+	0.00430555i
$779$			4.28571e48i			0.299148i
$780$	−6.82978e48	+	4.22156e48i	−0.466443	+	0.288313i
$781$	−1.65239e48			−0.110419
$782$	−6.93955e48	+	1.24476e49i	−0.453750	+	0.813901i
$783$		−	9.65955e48i		−	0.618026i
$784$	−4.92215e48	+	9.84702e48i	−0.308164	+	0.616498i
$785$	1.05958e49			0.649154
$786$	−7.65949e48	−	4.27017e48i	−0.459216	−	0.256013i
$787$		−	3.30427e49i		−	1.93868i	−0.245732	−	0.969338i	$-0.579028\pi$
$787$		−	3.30427e49i		−	1.93868i	0.245732	−	0.969338i	$-0.420972\pi$
$788$	1.38487e48	+	2.24049e48i	0.0795175	+	0.128646i
$789$	2.53435e48			0.142416
$790$	−1.17340e49	+	2.10475e49i	−0.645335	+	1.15755i
$791$			1.55560e49i			0.837331i
$792$	7.34872e47	−	3.31254e46i	0.0387154	−	0.00174515i
$793$	3.12758e49			1.61274
$794$	−2.21575e49	−	1.23528e49i	−1.11834	−	0.623473i
$795$			5.71226e48i			0.282206i
$796$	1.58690e48	−	9.80880e47i	0.0767410	−	0.0474344i
$797$	−3.23366e49			−1.53074			−0.765372	−	0.643589i	$-0.777445\pi$
$797$	−3.23366e49			−1.53074			−0.765372	+	0.643589i	$0.777445\pi$
$798$	2.88793e48	−	5.18013e48i	0.133825	−	0.240045i
$799$			9.68696e48i			0.439433i
$800$	5.20886e48	−	3.55346e48i	0.231320	−	0.157805i
$801$	−3.70527e48			−0.161090
$802$	−1.74112e49	−	9.70676e48i	−0.741080	−	0.413152i
$803$		−	2.69453e48i		−	0.112284i
$804$	1.30333e49	+	2.10857e49i	0.531743	+	0.860272i
$805$	2.15883e49			0.862358
$806$	−1.93221e49	+	3.46585e49i	−0.755717	+	1.35554i
$807$			5.81530e48i			0.222701i
$808$	−1.68318e48	−	3.73406e49i	−0.0631157	−	1.40019i
$809$	1.13694e49			0.417457			0.208729	−	0.977974i	$-0.433067\pi$
$809$	1.13694e49			0.417457			0.208729	+	0.977974i	$0.433067\pi$
$810$	−1.39817e48	−	7.79481e47i	−0.0502707	−	0.0280260i
$811$			1.72063e49i			0.605807i	0.953021	+	0.302903i	$0.0979560\pi$
$811$			1.72063e49i			0.605807i	−0.953021	+	0.302903i	$0.902044\pi$
$812$	8.33556e48	−	5.15229e48i	0.287397	−	0.177643i
$813$	5.67769e48			0.191704
$814$	−1.25101e48	+	2.24396e48i	−0.0413661	+	0.0741993i
$815$		−	2.58766e49i		−	0.837968i
$816$	9.26117e48	+	4.62931e48i	0.293720	+	0.146819i
$817$	1.19215e49			0.370301
$818$	1.31170e49	+	7.31275e48i	0.399052	+	0.222472i
$819$			1.10525e49i			0.329333i
$820$	5.95901e48	+	9.64070e48i	0.173916	+	0.281367i
$821$	−3.14575e49			−0.899270			−0.449635	−	0.893212i	$-0.648446\pi$
$821$	−3.14575e49			−0.899270			−0.449635	+	0.893212i	$0.648446\pi$
$822$	1.69148e49	−	3.03404e49i	0.473638	−	0.849574i
$823$		−	6.03104e49i		−	1.65423i	−0.562036	−	0.827113i	$-0.689982\pi$
$823$		−	6.03104e49i		−	1.65423i	0.562036	−	0.827113i	$-0.310018\pi$
$824$	−2.12964e48	+	9.59967e46i	−0.0572195	+	0.00257925i
$825$	−4.51044e47			−0.0118714
$826$	6.22950e47	+	3.47295e47i	0.0160617	+	0.00895442i
$827$			4.07466e49i			1.02919i	0.857432	+	0.514597i	$0.172058\pi$
$827$			4.07466e49i			1.02919i	−0.857432	+	0.514597i	$0.827942\pi$
$828$	3.68045e49	−	2.27492e49i	0.910721	−	0.562926i
$829$	1.59125e49			0.385755			0.192878	−	0.981223i	$-0.438218\pi$
$829$	1.59125e49			0.385755			0.192878	+	0.981223i	$0.438218\pi$
$830$	1.11179e49	−	1.99424e49i	0.264055	−	0.473641i
$831$		−	4.52364e48i		−	0.105262i
$832$	−4.39444e49	+	3.96978e48i	−1.00186	+	0.0905045i
$833$	−1.57711e49			−0.352287
$834$	1.82919e49	+	1.01977e49i	0.400346	+	0.223193i
$835$		−	6.29027e49i		−	1.34896i
$836$	1.26707e48	+	2.04991e48i	0.0266253	+	0.0430753i
$837$	−7.64058e49			−1.57323
$838$	3.27739e49	−	5.87873e49i	0.661272	−	1.18614i
$839$			9.09030e49i			1.79732i	0.438649	+	0.898658i	$0.355457\pi$
$839$			9.09030e49i			1.79732i	−0.438649	+	0.898658i	$0.644543\pi$
$840$	−7.06265e47	−	1.56682e49i	−0.0136842	−	0.303578i
$841$	−3.33206e49			−0.632676
$842$	4.29427e49	+	2.39406e49i	0.799068	+	0.445481i
$843$		−	4.73692e49i		−	0.863829i
$844$	−8.94008e48	+	5.52595e48i	−0.159779	+	0.0987610i
$845$	5.77187e47			0.0101100
$846$	1.43210e49	−	2.56878e49i	0.245853	−	0.440992i
$847$			3.29871e49i			0.555042i
$848$	−1.40354e49	+	2.80786e49i	−0.231471	+	0.463069i
$849$	−4.84846e49			−0.783742
$850$	7.88999e48	+	4.39867e48i	0.125013	+	0.0696947i
$851$			1.51111e50i			2.34689i
$852$	3.71251e49	+	6.00622e49i	0.565189	+	0.914383i
$853$	1.02853e50			1.53491			0.767457	−	0.641100i	$-0.221522\pi$
$853$	1.02853e50			1.53491			0.767457	+	0.641100i	$0.221522\pi$
$854$	−2.97490e49	+	5.33614e49i	−0.435200	+	0.780627i
$855$			2.66647e49i			0.382395i
$856$	−9.21549e49	+	4.15402e48i	−1.29558	+	0.0584002i
$857$	−4.17170e49			−0.574961			−0.287481	−	0.957786i	$-0.592818\pi$
$857$	−4.17170e49			−0.574961			−0.287481	+	0.957786i	$0.592818\pi$
$858$	2.75676e48	+	1.53689e48i	0.0372490	+	0.0207663i
$859$			5.60765e49i			0.742844i	0.928464	+	0.371422i	$0.121130\pi$
$859$			5.60765e49i			0.742844i	−0.928464	+	0.371422i	$0.878870\pi$
$860$	2.68173e49	−	1.65760e49i	0.348290	−	0.215281i
$861$	−1.09643e49			−0.139613
$862$	−3.74492e49	+	6.71733e49i	−0.467540	+	0.838636i
$863$		−	1.10970e50i		−	1.35838i	−0.733962	−	0.679190i	$-0.762331\pi$
$863$		−	1.10970e50i		−	1.35838i	0.733962	−	0.679190i	$-0.237669\pi$
$864$	−4.78792e49	−	7.01842e49i	−0.574664	−	0.842376i
$865$	4.28175e49			0.503903
$866$	−3.50867e49	−	1.95608e49i	−0.404891	−	0.225727i
$867$		−	4.19418e49i		−	0.474595i
$868$	−4.07540e49	−	6.59332e49i	−0.452204	−	0.731592i
$869$	9.47256e48			0.103070
$870$	1.50771e49	−	2.70441e49i	0.160876	−	0.288566i
$871$		−	1.51339e50i		−	1.58359i
$872$	1.89645e48	+	4.20720e49i	0.0194609	+	0.431730i
$873$	1.04176e49			0.104840
$874$	1.23806e50	+	6.90219e49i	1.22193	+	0.681228i
$875$		−	6.25511e49i		−	0.605478i
$876$	−9.79428e49	+	6.05394e49i	−0.929828	+	0.574736i
$877$	1.99502e50			1.85761			0.928804	−	0.370570i	$-0.120838\pi$
$877$	1.99502e50			1.85761			0.928804	+	0.370570i	$0.120838\pi$
$878$	8.49131e49	−	1.52310e50i	0.775475	−	1.39099i
$879$			3.36457e49i			0.301383i
$880$	5.70055e48	+	2.84949e48i	0.0500854	+	0.0250358i
$881$	−5.46277e49			−0.470785			−0.235392	−	0.971900i	$-0.575637\pi$
$881$	−5.46277e49			−0.470785			−0.235392	+	0.971900i	$0.575637\pi$
$882$	4.18217e49	+	2.33156e49i	0.353538	+	0.197097i
$883$		−	1.49088e50i		−	1.23626i	−0.786075	−	0.618131i	$-0.787890\pi$
$883$		−	1.49088e50i		−	1.23626i	0.786075	−	0.618131i	$-0.212110\pi$
$884$	−3.32351e49	−	5.37689e49i	−0.270339	−	0.437364i
$885$	2.25354e48			0.0179817
$886$	−8.98572e49	+	1.61179e50i	−0.703363	+	1.26164i
$887$			4.46950e49i			0.343208i	0.985166	+	0.171604i	$0.0548950\pi$
$887$			4.46950e49i			0.343208i	−0.985166	+	0.171604i	$0.945105\pi$
$888$	1.09672e50	−	4.94363e48i	0.826183	−	0.0372414i
$889$	5.00044e48			0.0369554
$890$	−2.80379e49	−	1.56312e49i	−0.203290	−	0.113334i
$891$			6.29256e47i			0.00447617i
$892$	−1.16135e50	+	7.17842e49i	−0.810514	+	0.500987i
$893$	9.63481e49			0.659733
$894$	−7.80885e48	+	1.40069e49i	−0.0524625	+	0.0941031i
$895$			1.54259e50i			1.01685i
$896$	3.50262e49	−	7.87522e49i	0.226546	−	0.509362i
$897$	1.85643e50			1.17817
$898$	−2.73915e50	−	1.52708e50i	−1.70576	−	0.950964i
$899$		−	1.53021e50i		−	0.935052i
$900$	−1.44197e49	−	2.33287e49i	−0.0864638	−	0.139884i
$901$	−4.49710e49			−0.264613
$902$	2.16943e48	−	3.89135e48i	0.0125266	−	0.0224693i
$903$			3.04991e49i			0.172820i
$904$	1.21632e49	+	2.69835e50i	0.0676370	+	1.50050i
$905$	−2.30241e50			−1.25648
$906$	1.11801e50	+	6.23289e49i	0.598777	+	0.333818i
$907$			2.13798e50i			1.12378i	0.827213	+	0.561888i	$0.189925\pi$
$907$			2.13798e50i			1.12378i	−0.827213	+	0.561888i	$0.810075\pi$
$908$	1.54304e50	−	9.53768e49i	0.796008	−	0.492021i
$909$	−1.62576e50			−0.823135
$910$	−4.66265e49	+	8.36349e49i	−0.231702	+	0.415608i
$911$			1.58427e50i			0.772710i	0.922350	+	0.386355i	$0.126266\pi$
$911$			1.58427e50i			0.772710i	−0.922350	+	0.386355i	$0.873734\pi$
$912$	4.60438e49	−	9.21130e49i	0.220424	−	0.440970i
$913$	−8.97520e48			−0.0421736
$914$	−8.72748e49	−	4.86557e49i	−0.402535	−	0.224413i
$915$			1.93037e50i			0.873940i
$916$	5.23824e49	+	8.47461e49i	0.232789	+	0.376614i
$917$	−1.04582e50			−0.456223
$918$	5.92677e49	−	1.06310e50i	0.253801	−	0.455247i
$919$			3.60550e49i			0.151566i	0.997124	+	0.0757830i	$0.0241456\pi$
$919$			3.60550e49i			0.151566i	−0.997124	+	0.0757830i	$0.975854\pi$
$920$	3.74471e50	−	1.68798e49i	1.54535	−	0.0696587i
$921$	−2.56737e50			−1.04010
$922$	−4.67180e49	−	2.60453e49i	−0.185806	−	0.103587i
$923$		−	4.31085e50i		−	1.68319i
$924$	−5.24437e48	+	3.24160e48i	−0.0201034	+	0.0124261i
$925$	9.57825e49			0.360476
$926$	3.12106e49	−	5.59831e49i	0.115323	−	0.206857i
$927$			9.27220e48i			0.0336378i
$928$	1.40561e50	−	9.58896e49i	0.500666	−	0.341551i
$929$	−1.09796e50			−0.383988			−0.191994	−	0.981396i	$-0.561495\pi$
$929$	−1.09796e50			−0.383988			−0.191994	+	0.981396i	$0.561495\pi$
$930$	−2.13915e50	−	1.19258e50i	−0.734567	−	0.409522i
$931$			1.56862e50i			0.528899i
$932$	−5.19858e49	−	8.41045e49i	−0.172113	−	0.278451i
$933$	1.12307e50			0.365107
$934$	−1.18696e49	+	2.12908e49i	−0.0378913	+	0.0679664i
$935$			9.13007e48i			0.0286205i
$936$	8.64197e48	+	1.91718e50i	0.0266026	+	0.590165i
$937$	−5.89876e50			−1.78315			−0.891575	−	0.452874i	$-0.850399\pi$
$937$	−5.89876e50			−1.78315			−0.891575	+	0.452874i	$0.850399\pi$
$938$	2.58208e50	+	1.43951e50i	0.766517	+	0.427333i
$939$			3.67351e49i			0.107094i
$940$	2.16735e50	−	1.33966e50i	0.620518	−	0.383549i
$941$	5.47279e50			1.53881			0.769405	−	0.638761i	$-0.220553\pi$
$941$	5.47279e50			1.53881			0.769405	+	0.638761i	$0.220553\pi$
$942$	−8.66680e49	+	1.55458e50i	−0.239328	+	0.429287i
$943$		−	2.62048e50i		−	0.710694i
$944$	1.10773e49	+	5.53711e48i	0.0295059	+	0.0147489i
$945$	−1.84376e50			−0.482351
$946$	−1.08245e49	−	6.03464e48i	−0.0278136	−	0.0155061i
$947$			1.85227e50i			0.467471i	0.972300	+	0.233735i	$0.0750949\pi$
$947$			1.85227e50i			0.467471i	−0.972300	+	0.233735i	$0.924905\pi$
$948$	−2.12825e50	−	3.44316e50i	−0.527572	−	0.853524i
$949$	7.02965e50			1.71162
$950$	4.37499e49	−	7.84751e49i	0.104635	−	0.187685i
$951$			2.12008e50i			0.498061i
$952$	1.23351e50	−	5.56023e48i	0.284652	−	0.0128311i
$953$	3.27186e50			0.741677			0.370839	−	0.928697i	$-0.379070\pi$
$953$	3.27186e50			0.741677			0.370839	+	0.928697i	$0.379070\pi$
$954$	1.19254e50	+	6.64840e49i	0.265552	+	0.148045i
$955$		−	3.92562e50i		−	0.858720i
$956$	−1.73732e50	+	1.07385e50i	−0.373332	+	0.230760i
$957$	−1.21714e49			−0.0256943
$958$	4.66205e49	−	8.36241e49i	0.0966859	−	0.173428i
$959$		−	4.14265e50i		−	0.844038i
$960$	−2.45019e49	−	2.71229e50i	−0.0490442	−	0.542906i
$961$	−7.01867e50			−1.38025
$962$	−5.85418e50	−	3.26371e50i	−1.13107	−	0.630572i
$963$			4.01231e50i			0.761637i
$964$	−2.06845e50	−	3.34642e50i	−0.385777	−	0.624123i
$965$	3.28409e50			0.601798
$966$	−1.76581e50	+	3.16737e50i	−0.317931	+	0.570280i
$967$		−	2.96151e50i		−	0.523918i	−0.965079	−	0.261959i	$-0.915631\pi$
$967$		−	2.96151e50i		−	0.523918i	0.965079	−	0.261959i	$-0.0843685\pi$
$968$	2.57926e49	+	5.72196e50i	0.0448346	+	0.994635i
$969$	1.47529e50			0.251985
$970$	7.88305e49	+	4.39481e49i	0.132305	+	0.0737599i
$971$			8.75750e49i			0.144429i	0.997389	+	0.0722143i	$0.0230066\pi$
$971$			8.75750e49i			0.144429i	−0.997389	+	0.0722143i	$0.976993\pi$
$972$	−5.12363e50	+	3.16697e50i	−0.830331	+	0.513236i
$973$	2.49755e50			0.397738
$974$	−3.66575e50	+	6.57533e50i	−0.573668	+	1.02900i
$975$		−	1.17671e50i		−	0.180964i
$976$	−4.74305e50	+	9.48872e50i	−0.716822	+	1.43404i
$977$	2.85606e50			0.424190			0.212095	−	0.977249i	$-0.431971\pi$
$977$	2.85606e50			0.424190			0.212095	+	0.977249i	$0.431971\pi$
$978$	3.79654e50	+	2.11658e50i	0.554151	+	0.308939i
$979$			1.26186e49i			0.0181012i
$980$	2.18106e50	+	3.52860e50i	0.307486	+	0.497461i
$981$	1.83176e50			0.253802
$982$	3.72997e50	−	6.69053e50i	0.507938	−	0.911098i
$983$		−	1.39848e50i		−	0.187174i	−0.995611	−	0.0935869i	$-0.970167\pi$
$983$		−	1.39848e50i		−	0.187174i	0.995611	−	0.0935869i	$-0.0298333\pi$
$984$	−1.90187e50	+	8.57297e48i	−0.250187	+	0.0112776i
$985$	9.92514e49			0.128328
$986$	2.12911e50	+	1.18698e50i	0.270576	+	0.150846i
$987$			2.46491e50i			0.307900i
$988$	−5.34794e50	+	3.30562e50i	−0.656627	+	0.405868i
$989$	−7.28933e50			−0.879732
$990$	1.34977e49	−	2.42110e49i	0.0160125	−	0.0287220i
$991$			1.13058e51i			1.31841i	0.751964	+	0.659205i	$0.229107\pi$
$991$			1.13058e51i			1.31841i	−0.751964	+	0.659205i	$0.770893\pi$
$992$	−7.58475e50	−	1.11182e51i	−0.869446	−	1.27449i
$993$	−2.43679e50			−0.274587
$994$	7.35499e50	+	4.10041e50i	0.814730	+	0.454212i
$995$		−	7.02981e49i		−	0.0765511i
$996$	2.01651e50	+	3.26237e50i	0.215869	+	0.349241i
$997$	5.59246e49			0.0588552			0.0294276	−	0.999567i	$-0.490632\pi$
$997$	5.59246e49			0.0588552			0.0294276	+	0.999567i	$0.490632\pi$
$998$	5.11683e50	−	9.17817e50i	0.529398	−	0.949592i
$999$		−	1.29057e51i		−	1.31271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.35.b.a.3.14	yes	16
4.3	odd	2	inner	4.35.b.a.3.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.35.b.a.3.13	✓	16	4.3	odd	2	inner
4.35.b.a.3.14	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(114483. + 63824.3i) q^{2} +8.29643e7i q^{3} +(9.03280e9 + 1.46136e10i) q^{4} +6.47366e11 q^{5} +(-5.29513e12 + 9.49799e12i) q^{6} +1.29684e14i q^{7} +(1.01400e14 + 2.24952e15i) q^{8} +9.79411e15 q^{9} +O(q^{10})\)	\(q+(114483. + 63824.3i) q^{2} +8.29643e7i q^{3} +(9.03280e9 + 1.46136e10i) q^{4} +6.47366e11 q^{5} +(-5.29513e12 + 9.49799e12i) q^{6} +1.29684e14i q^{7} +(1.01400e14 + 2.24952e15i) q^{8} +9.79411e15 q^{9} +(7.41124e16 + 4.13177e16i) q^{10} -3.33547e16i q^{11} +(-1.21240e18 + 7.49399e17i) q^{12} +8.70180e18 q^{13} +(-8.27701e18 + 1.48467e19i) q^{14} +5.37083e19i q^{15} +(-1.31965e20 + 2.64003e20i) q^{16} -4.22830e20 q^{17} +(1.12126e21 + 6.25102e20i) q^{18} +4.20554e21i q^{19} +(5.84753e21 + 9.46034e21i) q^{20} -1.07592e22 q^{21} +(2.12884e21 - 3.81855e21i) q^{22} -2.57146e23i q^{23} +(-1.86629e23 + 8.41259e21i) q^{24} -1.62993e23 q^{25} +(9.96207e23 + 5.55386e23i) q^{26} +2.19617e24i q^{27} +(-1.89515e24 + 1.17141e24i) q^{28} -4.39836e24 q^{29} +(-3.42789e24 + 6.14868e24i) q^{30} +3.47904e25i q^{31} +(-3.19575e25 + 2.18012e25i) q^{32} +2.76725e24 q^{33} +(-4.84068e25 - 2.69868e25i) q^{34} +8.39534e25i q^{35} +(8.84682e25 + 1.43127e26i) q^{36} -5.87647e26 q^{37} +(-2.68415e26 + 4.81462e26i) q^{38} +7.21938e26i q^{39} +(6.56431e25 + 1.45626e27i) q^{40} +1.01906e27 q^{41} +(-1.23174e27 - 6.86696e26i) q^{42} -2.83471e27i q^{43} +(4.87432e26 - 3.01287e26i) q^{44} +6.34038e27 q^{45} +(1.64121e28 - 2.94388e28i) q^{46} -2.29098e28i q^{47} +(-2.19028e28 - 1.09484e28i) q^{48} +3.72989e28 q^{49} +(-1.86599e28 - 1.04029e28i) q^{50} -3.50798e28i q^{51} +(7.86016e28 + 1.27164e29i) q^{52} +1.06357e29 q^{53} +(-1.40169e29 + 2.51424e29i) q^{54} -2.15927e28i q^{55} +(-2.91727e29 + 1.31500e28i) q^{56} -3.48909e29 q^{57} +(-5.03537e29 - 2.80722e29i) q^{58} -4.19589e28i q^{59} +(-7.84870e29 + 4.85136e29i) q^{60} +3.59417e30 q^{61} +(-2.22047e30 + 3.98291e30i) q^{62} +1.27014e30i q^{63} +(-5.05004e30 + 4.56202e29i) q^{64} +5.63325e30 q^{65} +(3.16803e29 + 1.76618e29i) q^{66} -1.73917e31i q^{67} +(-3.81934e30 - 6.17906e30i) q^{68} +2.13339e31 q^{69} +(-5.35826e30 + 9.61122e30i) q^{70} -4.95397e31i q^{71} +(9.93125e29 + 2.20320e31i) q^{72} +8.07839e31 q^{73} +(-6.72755e31 - 3.75061e31i) q^{74} -1.35226e31i q^{75} +(-6.14579e31 + 3.79878e31i) q^{76} +4.32559e30 q^{77} +(-4.60772e31 + 8.26496e31i) q^{78} +2.83994e32i q^{79} +(-8.54298e31 + 1.70907e32i) q^{80} -1.88656e31 q^{81} +(1.16665e32 + 6.50411e31i) q^{82} -2.69083e32i q^{83} +(-9.71854e31 - 1.57230e32i) q^{84} -2.73726e32 q^{85} +(1.80923e32 - 3.24525e32i) q^{86} -3.64907e32i q^{87} +(7.50320e31 - 3.38218e30i) q^{88} -3.78316e32 q^{89} +(7.25865e32 + 4.04670e32i) q^{90} +1.12849e33i q^{91} +(3.75782e33 - 2.32275e33i) q^{92} -2.88636e33 q^{93} +(1.46220e33 - 2.62278e33i) q^{94} +2.72252e33i q^{95} +(-1.80872e33 - 2.65133e33i) q^{96} +1.06366e33 q^{97} +(4.27009e33 + 2.38057e33i) q^{98} -3.26680e32i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots - 67\!\cdots\!80 q^{9}+O(q^{10}) \) 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9	\( 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots + 16\!\cdots\!32 q^{98}+O(q^{100}) \) 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9 - 45113792455239160 * q^10 + 2389205919902175360 * q^12 - 5233507036411659616 * q^13 - 78584294183795706432 * q^14 + 495182112183820124416 * q^16 - 603670905919309938144 * q^17 - 3049682100893194226508 * q^18 - 33058393758449688290400 * q^20 + 51436061805005728413696 * q^21 + 71660876143050404765280 * q^22 + 216144869785928938234368 * q^24 + 1224730607199300816400560 * q^25 - 2068583291215840445568696 * q^26 + 891252510406495618671360 * q^28 - 4086289565288128397679456 * q^29 + 29601064663371600024444480 * q^30 + 20026414012547463259849728 * q^32 + 73954448514753271238568960 * q^33 + 46288216238217191722231976 * q^34 + 569062048300724903070378384 * q^36 + 950385175701396416644593056 * q^37 - 123498782719680108073563360 * q^38 - 3250024485723791435879459200 * q^40 + 469238845433510127731349792 * q^41 + 2352670327884382399711157760 * q^42 + 7327222247557584897899214720 * q^44 - 24427097188106605438098250080 * q^45 - 19562783684402230406331003072 * q^46 + 10576141603633237485164267520 * q^48 - 5662649722408510114314091760 * q^49 + 20191932196464263485504736220 * q^50 - 299155663662273783907276503904 * q^52 - 287274278887575172234950512736 * q^53 + 6047252470624543429578889536 * q^54 + 957626384837555513184792726528 * q^56 + 2791286265941381406754467578880 * q^57 - 314499391713380785247660833336 * q^58 + 1103184540481814815474103512320 * q^60 - 7360215904797065436447249778528 * q^61 + 6668101684324825273374014288640 * q^62 - 4672502276277215477475812569088 * q^64 + 7390500022468645317433010287680 * q^65 - 12460359580334220374288279205120 * q^66 + 3201090312765007118305938045984 * q^68 - 20909099675706939600670541666304 * q^69 - 13302319794857519494110175324800 * q^70 - 776423968147266229824274003392 * q^72 - 21322365514881309087265291408096 * q^73 + 60200090281780873185690769101576 * q^74 - 104909582027053727863743869884800 * q^76 + 31510097566037837419459121448960 * q^77 + 173718506967281862717403400063040 * q^78 + 360511559214548868760655536888320 * q^80 - 262819454584631237298859074129648 * q^81 - 127799686177535642546403976474264 * q^82 - 481860976739335096182940424300544 * q^84 + 2066519418228326883252673443837760 * q^85 + 680164732953303409567751182232928 * q^86 - 1868588957981221169228370505105920 * q^88 - 2487774705888249186282098457137376 * q^89 + 2710136859758550244207319911170120 * q^90 - 5719642193953545223478177490435840 * q^92 - 4648987096869411453766406983557120 * q^93 - 174301665834847119752293250078592 * q^94 - 1356265248520894619800195113541632 * q^96 + 7119191713926779638291321673063456 * q^97 + 16929214407930779244441537548523732 * q^98

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